Nell’ambito del programma “Visiting Professor 2016” finanziato dalla Regione Autonoma della Sardegna, la Prof.ssa. Irene I. ONNIS (Università di San Paolo, Brasile) terrà le seguenti lezioni
28 Settembre ore 16 Aula B
Title: Helix surfaces in the Berger sphere and in the special linear group
Abstract: In recent years much work has been done to understand the geometry of surfaces whose unit normal vector field forms a constant angle with a fixed field of directions of the ambient space. These surfaces are called helix surfaces or constant angle surfaces and they have been studied in most of the three-dimensional geometries. In this talk, we present a characterization of helix surfaces in the Berger sphere. In particular, we prove that a helix surface is invariant by the action of a one-parameter group of isometries of the ambient space. Also, we discuss some recent results about helix surfaces in the special linear group SL(2,R).
4 Ottobre ore 16 Aula B
Title: Enneper representation of minimal surfaces in the Lorentz-Minkowski 3-space
Abstract: In the Lorentz-Minkowski 3-space a Weierstrass representation type theorem was proved by Kobayashi (in 1983) for spacelike minimal immersions and by Konderak (in 2005) for the case of timelike minimal surfaces. Recently, these theorems were extended for immersed minimal surfaces in Riemannian and Lorentzian 3-dimensional manifolds by Lira, Melo and Mercuri. In this talk, we prove an Enneper-type representation for spacelike and timelike minimal surfaces in the Lorentz-Minkowski space. Then, we exhibit some examples of minimal surfaces in this space constructed via the Enneper representation formula, that it is equivalent to the Weierstrass representation obtained by Kobayashi and by Konderak, respectively.
Proff. Angela Slavova and Petar Popivanov (Bulgarian Academy of Sciences)
May 3-5, 2016, 15:00-18:00
Contact Francesco Demontis for more information
La scuola 12TH SEMANTIC WEB SUMMER SCHOOL – SSSW 2016 si terrà a Bertinoro (Bologna) dal 17 al 23 luglio 2016. Maggiori informazioni in questa pagina web.
Prof. Sebastian Heller (University of Tubingen)
November 17-18, 16-18 hr., Palazzo delle Scienze
Contact Stefano Montaldo for more information.
In these lectures I will talk about constant mean curvature (CMC) surfaces of higher genus in space forms from the integrable systems point of view. CMC surfaces are characterized by the harmonicity of their Gauss map and hence deliver an associated family of CMC surfaces (with periods). After recalling the general gauge theoretic description of CMC surfaces and their associated families, I will explain the recent spectral curve approach to CMC surfaces of higher genus. I will introduce a flow on the spectral data which turns out to be a powerful tool for a detailed study of the moduli space of CMC surfaces. Finally, I will report about numerical experiments and about the visualization of CMC surfaces. These lectures are partially based on joint work with Lynn Heller and Nicholas Schmitt.
Plan of the course
- Lezione 1 (martedì 5 maggio 17-19) Strutture complesse e forme simplettiche.
- Lezione 2 (mercoledì 6 maggio 17-19) Metriche a curvature costante su varietà reali e superfici di Riemann.
- Lezione 3 (giovedì 7 maggio 17-19) Varieta’ Kahleriane: coomologia, fibrati lineari, classi di Chern e curvatura.
- Lezione 4 (venerdì 8 maggio 17-19) Varieta’ Kahleriane di Einstein. ddbar-Lemma e Congeture di Calabi. Teorema di Yau (con cenni di dimostrazione).