Pseudo-spherical submanifolds with 1-type pseudo-spherical gauss map
Künye
Bektaş, B., Canfes, E. Ö. & Dursun, U. (2016). Pseudo-spherical submanifolds with 1-type pseudo-spherical gauss map. Results in Mathematics, 71(3-4), 867-887. doi:10.1007/s00025-016-0560-9Özet
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.