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Yayın On submanifolds of pseudo-hyperbolic space with 1-type pseudo-hyperbolic gauss map(B. I. Verkin Institute for Low Temperature Physics and Engineering, 2016) Dursun, Uğur; Yeğin, RüyaIn this paper, we examine pseudo-Riemannian submanifolds of a pseudo-hyperbolic space ?m-1 s (-1) ? Em s+1 with finite type pseudo-hyperbolic Gauss map. We begin by providing a characterization of pseudo-Riemannian sub- manifolds in ?m-1 s (-1) with 1-type pseudo-hyperbolic Gauss map, and we obtain the classification of maximal surfaces in ?m-1 2 (-1) ? Em 3 with 1-type pseudo-hyperbolic Gauss map. Then we investigate the submanifolds of ?m-1 s (-1) with 1-type pseudo-hyperbolic Gauss map containing nonzero constant component in its spectral decomposition.Yayın Hyperbolic submanifolds with finite type hyperbolic Gauss map(World Scientific Publishing Co. Pte Ltd, 2015-02) Dursun, Uğur; Yeğin, RüyaWe study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface M-n with nonzero constant mean curvature in a hyperbolic space Hn+1 subset of E-1(n+2) has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space H-3 subset of E-1(4) having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in Hn+1 subset of E-1(n+2) has biharmonic hyperbolic Gauss map.
