FACULTY of ENGINEERING and NATURAL SCIENCES

Faculty of Engineering and Natural Sciences Seminar

09.06.2016

Dr. Rüya YEĞİN ŞEN will given a speech in Meeting Room of Faculty of Engineering and Natural Sciences on "HYPERBOLIC SUBMANIFOLDS WITH FINITE TYPE HYPERBOLIC GAUSS MAP" in 09.06.2016.

ABSTRACT:

In this work, firstly, by using the definition of generalized Gauss map in Obata's sense, the definition of hyperbolic Gauss map and pseudo-hyperbolic Gauss map are given.  We characterize and classify submanifolds of the hyperbolic space with 1-type hyperbolic Gauss map.  Moreover, we classify submanifolds of with 1-type hyperbolic Gauss map such that its spectral decomposition contains a constant component.  For hypersurfaces with non-zero constant mean curvature of hyperbolic space having 2-type hyperbolic Gauss map is obtained.  On the other hand, we show that a horohypersurface in   has biharmonic hyperbolic Gauss map. We also classify surfaces with constant mean curvature in the 3-dimensional hyperbolic space   having 2-type hyperbolic Gauss map.