Publication
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EELLS, J. and SAMPSON, J.H. (1964). Harmonic mappings of Riemannian manifolds.
Amer. J. Math. 86, 109–160.
MR 0164306 Harmonic maps -
EELLS, J. and SAMPSON, J.H. (1964). Energie et deformations en geometrie differentielle.
Ann. Inst. Fourier, 14, 61–70.
MR
0172310Zbl 0123.38703Intrisic (p. 67) -
EELLS, J. and SAMPSON, J.H. (1965). Variational theory in fibre bundles.
US-Japan Seminar in Diff. Geom., 22–33.
MR
0216519Zbl 0192.29801Intrisic (p. 29, theorem erroneous) -
EELLS, J. (1966). A setting for global analysis.
Bull. Amer. Math. Soc., 72, 751–807.MR
0203742Zbl 0000.00000Intrinsic (p. 792, statement p. 792-793 erroneous) -
ELIASSON, H.I. (1967). Geometry of manifolds of maps.
J. Diff. Geom., 1, 169–194.
MR
0226681Zbl 0163.43901Extrinsic (p.194) -
PALAIS, R.S. (1971). Banach manifolds of fibre bundle sections.
Actes du Congres International des Mathematiciens (Nice, 1970) Tome 2 243–249.
MR
0448405Zbl 0326.58008Intrisic/extrinsic (closing statement unclear) -
LEMAIRE, L. (1981). Minima and critical points of the energy in dimension two.
Global Differential Geometry and Global Analysis (Berlin 1979) 187–193.
MR
0636281Zbl 0437.58005Shows that E_{2} + tE does not satisfy condition (C) (p. 190) -
EELLS, J. (1984). Certain variational principles in Riemannian geometry.
Proc. Int. Colloq. Diff. Geom. Santiago de Compostela, 46–60.
MR
0864856Zbl 0653.53026Intrisic (p. 55) -
JIANG, G.Y. (1986). 2-harmonic isometric immersions between Riemannian manifolds.
Chinese Ann. Math. Ser. A, 7, 130–144.
MR 0858581 Intrinsic -
JIANG, G.Y. (1986). 2-Harmonic maps and their first and second variational formulas.
Chinese Ann. Math. Ser. A, 7, 389–402.
MR 0886529 Intrinsic, First Variation -
JIANG, G.Y. (1987). The conservation law for 2-harmonic maps between Riemannian manifolds.
Acta Math. Sinica 30, 220–225.
MR 0891928 Intrinsic, submanifolds -
JIANG, G.Y. (1987). Some nonexistence theorems on 2-harmonic and isometric immersions in Euclidean space.
Chinese Ann. Math. Ser. A 8, 377–383.
MR 0924896 Intrinsic, submanifolds -
DIMITRIC, I.M. (1988). Quadric representation and submanifolds of finite type.
Doctoral dissertation, Michigan State University.
MR 000000 Intrinsic, submanifolds, curves -
CHEN, B.-Y. (1991).
Some open problems and conjectures on submanifolds
of finite type.Soochow J. Math., 17, 169–188.MR 1143504 Intrinsic, submanifold, curves -
CHEN, B.-Y. and ISHIKAWA, S. (1991). Biharmonic surfaces in pseudo-Euclidean spaces.
Mem. Fac. Sci. Kyushu Univ. Ser. A, 45, 323–347.
MR 1133117 Intrinsic, semi-Riemannian, submanifold -
ISHIKAWA, S. (1992). On biharmonic submanifolds and finite type
submanifolds in a Euclidean space or a pseudo-Euclidean space.Doctoral Thesis, Kyushu Univ., Fukuota.
MR 000000 Intrinsic, submanifolds, curves -
ISHIKAWA, S. (1992). Biharmonic W-surfaces in 4-dimensional pseudo-Euclidean space.
Mem. Fac. Sci. Kyushu Univ. Ser. A, 46, 269–286.
MR 1195470 Intrinsic, submanifolds, curves -
DIMITRIC, I. (1992). Submanifolds of E^m with harmonic mean
curvature vector.Bull. Inst. Math. Acad. Sinica, 20, 53–65.
MR 1166218 Intrinsic, submanifolds, curves -
SUN, H.A. (1992). A theorem on 2-harmonic mappings.
J. Math. (Wuhan) 12, 103–106.
MR 1204581 Intrinsic -
SUN, H.A. (1992). Compositions of 2-harmonic maps.
J. Math. Res. Exposition 12, 535–538.
MR 1193402 Intrinsic -
FERRANDEZ, A. and LUCAS, P. (1992). Null 2-type hypersurfaces in a Lorentz space.
Canad. Math. Bull., 35, 354–360.
MR 1184012 Intrinsic, second variation -
CHEN, J.H. (1993). Compact 2-harmonic hypersurfaces in S^{n+1}(1).
Acta Math. Sinica 36, 341–347.
MR 1247088 Intrinsic, submanifolds -
SUN, H.A. (1993). 2-harmonic isometric immersions with parallel mean curvature vector.
J. Math. (Wuhan) 13, 141–146.
MR 1257740 Intrinsic, submanifolds -
GARAY, O.J. (1994). A classification of certain 3-dimensional conformally flat Euclidean hypersurfaces.
Pacific J. Math. 162, 13–25.
MR 1247141 Intrinsic, submanifolds -
ALIAS, L.J. (1994). Characterization and Classification of Hypersurfaces in Pseudo-Riemannian Space Forms.
Doctoral dissertation, Universidad de Murcia.
MR 0000000 Intrinsic, submanifolds, semi-Riemannian -
SUN, H.A. (1994). 2-harmonic isometric immersions in a sphere with parallel mean curvature vector.
Pure Appl. Math. (Xi’an) 10, 114–118.
MR 1306920 Intrinsic, submanifolds -
ALIAS, L.J.; FERRANDEZ, A. and LUCAS, P. (1995). Hypersurfaces in the non-flat Lorentzian space forms with a characteristic eigenvector field.
J. Geom. 52, 10–24.
MR 1317251 Intrinsic, submanifolds -
SUN, H.A. (1995).
2-harmonic totally real submanifolds in a complex projective space.Chin. Q. J. Math. 10, 37–41.MR Intrinsic, submanifolds -
ZHONG, D.S. (1995).
2-harmonic isometric immersions of 3-dimensional submanifolds
with parallel mean curvature vector.Natur. Sci. J. Harbin Normal Univ. 11, 8–12.MR 1433300 Intrinsic, submanifolds -
CHEN, B.-Y. and VERSTRAELEN, L. (1995). Laplace transformations of submanifolds.
Centre for Pure and Applied Differential Geometry (PADGE), 1.MR 1347686 Intrinsic, submanifold, semi-Riemannian -
HASANIS, T. and VLACHOS, T. (1995). Hypersurfaces in E^4 with
harmonic mean curvature vector field.Math. Nachr., 172, 145–169.
MR 1330627 Intrinsic, submanifold -
FERRANDEZ, A. and MERONO, M. A. (1996). Biharmonic products in the normal bundle.
Comment. Math. Univ. St. Paul., 45, 147–158.
MR 1416188 Intrinsic, submanifold, semi-Riemannian -
CHEN, B.-Y. (1996). A report on submanifolds of finite type.
Soochow J. Math., 22, 117–337.
MR 1391469 Intrinsic, submanifold, curves -
CHEN, B.-Y. and ISHIKAWA, S. (1998). Biharmonic pseudo-Riemannian submanifolds in pseudo-Euclidean spaces.
Kyushu J. Math., 52, 167–185.
MR 1609044 Intrinsic, semi-Riemannian, submanifold -
CHIANG, Y.-J. and SUN, H.A. (1999).
2-harmonic totally real submanifolds in a complex projective space.Bull. Inst. Math. Acad. Sinica 27, 99–107.MR 1697219 Intrinsic, submanifolds -
SUN, H.A. and ZHONG, D.X. (1999). Real 2-harmonic hypersurfaces in complex projective spaces.
J. Math. Res. Exposition 19, 431–436.
MR 1699561 Intrinsic, submanifolds -
CHANG, S.-Y. A.; WANG, L. and YANG, P. (1999). A regularity theory of biharmonic maps.
Comm. Pure Appl. Math. 52, 1113–1137.
MR 1692152 Extrinsic -
OU, Y.-L. (1999).
Biharmonic morphisms between Riemannian manifolds.Geometry and topology of submanifolds, X (Beijing/Berlin,
1999), 231–239.MR 1801915 Intrinsic -
SUN, H.A. and CHIANG, Y.J. (2000). 2-harmonic maps between V-manifolds.
J. Math. (Wuhan) 20, 139–144.
MR 1766459 Intrinsic -
YU, Y.B. (2000). Regularity of Intrinsic Biharmonic Maps to Spheres.
Doctoral dissertation, University of California, Los Angeles.
MR 000000 Intrinsic, regularity -
MOU, L. (2000). Existence of biharmonic curves and symmetric biharmonic maps.
Differential equations and computational simulations (Chengdu, 1999),
World Sci. Publishing, River Edge, NJ, 284–291.MR 1774479 Intrinsic, curves -
HONG, S.-H. and SONG, W.-D (2000). On the 2-harmonic hypersurfaces in a locally symmetric space.
J. Anhui Norm. Univ., Nat. Sci. 23, 313–316.
MR Intrinsic, submanifolds -
OUYANG, C.Z. (2000). 2-harmonic space-like submanifolds of a pseudo-Riemannian space form.
Chinese Ann. Math. Ser. A 21, 649–654.
MR 1813374 Intrinsic, submanifolds, semi-Riemannian -
CADDEO, R.; MONTALDO, S. and ONICIUC C. (2001). Biharmonic submanifolds of S^3.
Int. J. Math., 12, 867–876.
MR 1863283 Intrinsic, submanifold, curves -
CADDEO, R.; MONTALDO, S. and PIU, P. (2001). Biharmonic curves on a surface.
Rend. Mat. Appl., 21, 143–157.
MR 1884940 Intrinsic, curves -
CADDEO, R.; MONTALDO, S. and PIU, P. (2001).
On Biharmonic Maps.Contemporary Mathematics, 288, 286–290.MR 1871019 Intrinsic, curves -
Chiang, Y.J. and Sun, H.A. (2001). Biharmonic maps of V-Manifolds.
Inter. J. of Math and Math Sciences, 27, 477-484
MR Extrinsic -
LOUBEAU, E. and OU, Y.-L. (2001). The characterization of biharmonic morphisms.
Differential Geometry and its
Applications (Opava, 2001), Math. Publ., 3, 31–41.MR 1978760 Intrinsic -
CADDEO, R.; MONTALDO, S. and ONICIUC C. (2002). Biharmonic submanifolds in spheres.
Israel J. Math., 130, 109–123.
MR 1919374 Intrinsic, submanifold, curves -
CADDEO, R.; MONTALDO, S. and ONICIUC C. (2002). Biharmonic immersions into spheres.
Differential geometry, Valencia,
World Sci. Publishing, River Edge, NJ, 97–105.MR 1922040 Intrinsic, submanifold, curves -
SONG, W.D. (2002). 2-harmonic submanifolds of a locally symmetric space.
Math. Appl. (Wuhan) 15, 25–29.
MR 1889134 Intrinsic, submanifolds -
SUN, H.A.; ZHONG, D.X. and WU, Q.Q. (2002). 2-harmonic hypersurfaces in a de Sitter space.
J. Math. (Wuhan) 22, 83–86.
MR 1897104 Intrinsic, submanifolds, semi-Riemannian -
ONICIUC, C. (2002).
Tangency and harmonicity properties.Doctoral dissertation “Al. I. Cuza” University, Iasi.MR 2159756 Intrinsic -
ONICIUC, C. (2002). Biharmonic maps between Riemannian manifolds.
An. Stiint. Univ. Al.I.~Cuza Iasi Mat. (N.S.), 48, 237–248.
MR 2004799 Intrinsic -
BELKHELFA, M.; HIRICA, I.E.; ROSCA, R. and VERSTRAELEN, L. (2002). On Legendre curves in Riemannian and Lorentzian Sasaki spaces.
Soochow J. Math., 28 81–91.
MR 1893607 Intrinsic, curves -
ONICIUC, C. (2002). On the second variation formula for biharmonic maps to a sphere.
Publ. Math. Debrecen, 61, 613–622.
MR 1943720 Intrinsic, second variation -
SUN, H.A. and ZHONG, D.X. (2003). 2-harmonic submanifolds in pseudo-Riemannian manifolds.
J. Math. (Wuhan) 23, 117–120.
MR 1973139 Intrinsic, submanifolds, semi-Riemannian -
BAIRD, P. and KAMISSOKO, D. (2003).
On constructing biharmonic maps and metrics.Ann. Global Anal. Geom., 23, 65–75.MR 1952859 Intrinsic -
JAVALOYES, M. A. and MERONO , M. A. (2003). Biharmonic lifts by means of pseudo-Riemannian submersions in dimension thre.
Trans. Amer. Math. Soc., 355, 169–176.
MR 1928083 Submanifolds, semi-Riemannian -
SHU, S.C. and LIU, S.Y. (2003). 2-harmonic space-like submanifolds in de Sitter space.
Gongcheng Shuxue Xuebao 20, 135–138.
MR 1975353 Intrinsic, submanifolds, semi-Riemannian -
ONICIUC, C. (2003). New examples of biharmonic maps in spheres.
Colloq. Math., 97, 131–139.
MR 2010548 Intrinsic -
STRZELECKI, P. (2003). On biharmonic maps and their generalizations.
Calc. Var., 18, 401–432.
MR 2020368 Intrinsic, regularity -
EKMEKCI, N. and YAZ, N. (2003). Biharmonic general helices and submanifolds in an indefinite-Riemannian manifold.
Tensor (N.S.), 64, 282–289.
MR 2080341 Intrinsic, curves -
INOGUCHI, J.-I. (2003). Biharmonic curves in Minkowski 3-space.
Int. J. Math. Math. Sci., 21, 1365–1368.
MR 1990566 Intrinsic, curves -
KILLIC, B.; ARSLAN, K.; LUMISTE, U. and MURATHAN, C. (2003). On weak biharmonic submanifolds and 2-parallelity.
Differ. Geom. Dyn. Syst., 5, 39–48.
MR 1951456 Intrinsic, submanifolds, curves -
BALMUS, A. (2004). Biharmonic properties and conformal changes.
An. Stiint. Univ. Al.I. Cuza Iasi Mat. (N.S.), 50, 361–372.
MR 2131943 Intrinsic -
EKMEKCI, N. and YAZ, N. (2004). Biharmonic general helices in contact and Sasakian manifolds.
Tensor (N.S.), 65, 103–108.
MR 2104451 Intrinsic, curves -
BALMUS, A. (2004). On the biharmonic curves of the Euclidian and Berger 3-dimensional spheres.
Sci. Ann. Univ. Agric. Sci. Vet.
Med., 47, 87–96.MR 2148103 Intrinsic, curves -
ONICIUC, C. (2004). Biharmonic maps in spheres and conformal changes.
Recent advances in geometry and
topology, Cluj Univ. Press, Cluj-Napoca, 279–282.MR 2113592 Intrinsic -
CADDEO, R.; ONICIUC, C. and PIU, P. (2004). Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group.
Rend. Sem. Mat. Univ. Politec. Torino, 62, 265–278.
MR 2129448 Intrinsic, curves -
INOGUCHI, J. (2004). Submanifolds with harmonic mean curvature in contact 3-manifolds.
Colloq. Math., 100, 163–179.
MR 2107514 Intrinsic, submanifold, curves -
LAMM, T. (2004). Heat flow for extrinsic biharmonic maps with small initial energy.
Ann. Global. Anal. Geom., 26, 369–384.
MR 2103406 Extrinsic, heat flow -
WANG, C. (2004). Biharmonic maps from R^4 into a Riemannian manifold.
Math. Z., 247, 65–87.
MR 2054520 Extrinsic, Intrinsic -
WANG, C. (2004). Stationary biharmonic maps from R^m into a Riemannian manifold.
Comm. Pure Appl. Math., 57, 419–444.
MR 2026177 Intrinsic, extrinsic -
WANG, C. (2004). Remarks on biharmonic maps into spheres.
Calc. Var., 21, 221–242.
MR 2094320 Intrinsic, extrinsic -
ZHANG, Y. (2004).
On 2-harmonic submanifolds in Riemannian manifolds.J. Zhejiang Univ. Sci. Ed. 31, 605–609.MR 2110991 Intrinsic, submanifolds, -
LAMM, T. (2005). Biharmonic Maps.
Doctoral dissertation, Albert-Ludwigs-Universitat Freiburg im Breisgau.MR 000000 Intrinsic, submanifolds, curves -
BALMUS, A. and ONICIUC, C. (2005). Some remarks on the biharmonic submanifolds of S^3 and their stability.
An. Stiint. Univ.
Al.I. Cuza Iasi, Mat. (N.S), 51, 171–190.MR 000000 Intrinsic, submanifold, curves -
LOUBEAU, E. and ONICIUC, C. (2005). The index of biharmonic maps in spheres.
Compositio Math., 141, 729–745.
MR 2135286 Intrinsic, second variation -
LOUBEAU, E. and ONICIUC, C. (2005). The biharmonic index of the Hopf map.
Tensor (N.S.), 66, 1–8.
MR 2165169 Intrinsic, second variation -
SASAHARA, T. (2005) Legendre surfaces in Sasakian space forms whose mean curvature vectors
are eigenvectors.Pub. Math. Debracen, 67 285–303.
MR 000000
Zbl 000000Intrinsic -
LOUBEAU, E.; MONTALDO, S. (2005).
Examples of biminimal surfaces of Thurston’s three-dimensional geometries.Mat. Contemp., 29, 1–29.MR0000000 Intrinsic, submanifolds -
ANGELSBERG, G. (2006). A monotonicity formula for stationary biharmonic maps.
Math. Z., 252, 287–293.
MR
0000000Zbl 0000.00000Extrinsic, singularities, monotonicity -
FETCU, D. (2005) Biharmonic curves in the generalized Heisenberg group.
Beitrage zur algebra und geometrie 46, 513–521
MR 00000 Intrinsic, curves -
LOUBEAU, E. and ONICIUC, C. (to appear) On the biharmonic and harmonic indices of the Hopf map.
Trans. Amer. Math. Soc..
MR 000000
Zbl 000000Intrinsic, second variation -
DEFEVER, F.; KAIMAKAMIS G. and PAPANTONIOU, B.J. (2006) Biharmonic hypersurfaces of the 4-dimensional semi-Euclidean space E^4_s.
J. Math. Anal. Appl. 315 276-286.MR 000000
Zbl 000000Intrinsic, semi-Riemannian, submanifolds -
OU, Y.L. (to appear) p-harmonic morphisms, biharmonic morphisms, and nonharmonic biharmonic maps.
J. Geom. Phys..
MR 000000
Zbl 000000Intrinsic -
ARVANITOYEORGOS, A.; DEFEVER, F.; KAIMAKAMIS G.; PAPANTONIOU, B.J. (to appear) Biharmonic Lorentz hypersurfaces in E_1^4.
Pacific J. Math.
MR 000000
Zbl 000000Intrinsic, semi-Riemannian, submanifolds -
ARSLAN, K.; EZENTAS, R.; MURATHAN, C. and SASAHARA, T.
(2006)Biharmonic submanifolds in 3-dimensional (k,mu)-manifolds.Internat. J. Math. Math. Sci.
MR 000000
Zbl 000000Intrinsic, curves -
BEJAN, C.-L. and URAKAWA, H. (preprint). Yang-Mills fields analogues of biharmonic maps.
.MR
0000000Zbl 0000.00000Also contains short survey of (intrinsic) biharmonic maps. -
ARSLAN, K.; EZENTAS, R.; MURATHAN, C. and SASAHARA, T. (preprint) Biharmonic anti-invariant submanifolds in Sasakian
space forms.MR 000000
Zbl 000000Intrinsic, curves -
BALMUS, A.; MONTALDO, S and ONICIUC, C. (preprint) Biharmonic maps between warped product manifolds.
MR 000000
Zbl 000000Intrinsic -
CADDEO, R.; MONTALDO, S.; ONICIUC, C. and PIU, P. (preprint) The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional space.
MR 000000
Zbl 000000Intrinsic, curves -
CHO, J.T.; INOGUCHI, J. and LEE, J.E. (preprint) Biharmonic curves in 3-dimensional Saskian space forms.
MR 000000
Zbl 000000Intrinsic, curves -
LOUBEAU, E. and MONTALDO, S. (preprint) Biminimal immersions.
MR 000000 Intrinsic, submanifolds -
SASAHARA, T. (preprint) Stability of biharmonic Legendre submanifolds in Sasakian space forms.
MR 000000
Zbl 000000Intrinsic -
LOUBEAU, E.; MONTALDO, S.; ONICIUC, C.(2006). The stress-energy tensor for biharmonic maps.
math.DG/0602021.
MR0000000 Intrinsic -
SASAHARA, T. Biminimal Legendrian surfaces in 5-dimensional Sasakian
space forms.
Colloq. Math. 108 (2007), 297-304MR 000000
Zbl 000000Intrinsic -
CHEN, B-Y. (preprint) Classification of marginally trapped Lorentzian flat surfaces in
E^4_2 and its application to biharmonic surfacesMR 000000
Zbl 000000Intrinsic -
BALMUS, A.; MONTALDO, S.; ONICIUC, C.(2007). Classification results for biharmonic submanifolds in spheres.
math.DG/0701155.
MR0000000 Intrinsic