Workshop on Harmonic Maps and Curvature Properties of Submanifolds, 2

Short Plenary Talks

M. Haskins, "Special Lagrangian cones in dimension 3",

Abstract: We study isolated singularities of special Lagrangian (SLG) varieties with an emphasis on dimension 3. One of our main results is the construction of an infinite family of new 3-dimensional SLG cones. The links of these cones are all tori, which are themselves geometrically interesting. They show, for example, the sharpness of some pinching results of Yau (circa 1974) on minimal Lagrangian and Legendrian immersions.

S. Ianus, "Semi-Riemannian Submersions from real and complex pseudo-hyperbolic spaces"

Abstract: We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian submersions from a complex pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are complex, connected and totally geodesic submanifolds.

J. Inoguchi, "Minimal surfaces in 3-dimensional homogeneous spaces",

Abstract: Harmonic maps, in particular minimal surfaces, in three dimensional space forms has been studied extensively. On the other hand studies of such maps into 3-dimensional non symmetric homogeneous spaces has just started recently. For example, rotational minimal surfaces in the Heisenberg group or real special linear group SL(2;R) are classified by Caddeo-Piu-Ratto (1995) and Kokubu (1997). In this talk I would like to report the following topics:

(1) Representation formulae for minimal surfaces in Heisenberg group and Minkowski motion group;
(2) One parametric deformations of nonparametric minimal surfaces in Heisenberg group. (Joint work with Y. Suyama)