Faculty of Engineering and Natural Sciences Seminar
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.