Pseudo-Spherical Submanifolds with 1-Type Pseudo-Spherical Gauss Map
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CitationBektaş, B., Canfes, E. Ö., & Dursun, U. (2016). Pseudo-spherical submanifolds with 1-type pseudo-spherical gauss map. Results in Mathematics, , 1-21. doi:10.1007/s00025-016-0560-9
In this work, we study pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify Lorentzian surfaces in a 4-dimensional pseudo-sphere (Formula presented.) with index s, (Formula presented.), and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere (Formula presented.) with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space (Formula presented.) with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition.