Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map

2015/10/28 by Bektaş, Burcu, Canfes, Elif Özkara, Dursun, Uğur
#53B25 #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.08399

Abstract

In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere \mathbbS⁴_s(1) with index s, s=1, 2, and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere \mathbbS^m-1_s(1)⊂𝔼^m_s with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space \mathbbS⁴₁(1)⊂𝔼⁵₁ 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.

Related

• Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map
• Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space
• Wave maps and constant curvature surfaces: singularities and bifurcations
• Space-like Surfaces in Minkowski Space \mathbb E⁴₁ with Pointwise 1-Type Gauss Map
• On the quasi-minimal surfaces in the 4-dimensional de Sitter space with 1-type Gauss map