Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures

Uğur Dursun; Nurettin Cenk Turgay

Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures

Differential Geometry 2015-08-18 v1

Authors: Uğur Dursun , Nurettin Cenk Turgay

Abstract

In this paper we consider Lorentzian surfaces in the 4-dimensional pseudo-Riemannian sphere $\mathbb S^4_2(1)$ with index 2 of curvature one. We obtain the complete classification of minimal Lorentzian surfaces $\mathbb S^4_2(1)$ whose Gaussian and normal curvatures are constants. We conclude that such surfaces have the Gaussian curvature $1/3$ and the absolute value of normal curvature $2/3$ . We also give some explicit examples.

Keywords

minimal surfaces Lorentzian surfaces pseudo-Riemannian sphere Gaussian curvature normal curvature classification

Cite

@article{arxiv.1508.03824,
  title  = {Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures},
  author = {Uğur Dursun and Nurettin Cenk Turgay},
  journal= {arXiv preprint arXiv:1508.03824},
  year   = {2015}
}

Comments

Keywords. Gaussian curvature, minimal submanifolds, Lorentzian surfaces, normal curvature

Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures

Abstract

Keywords

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