×

zbMATH — the first resource for mathematics

Classification of minimal Lorentzian surfaces in \(\mathbb{S}^4_2(1)\) with constant Gaussian and normal curvatures. (English) Zbl 1357.53026
Summary: In this paper we consider Lorentzian surfaces in the \(4\)-dimensional pseudo-Riemannian sphere \(\mathbb{S}^4_2(1)\) with index \(2\) and 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.

MSC:
53B25 Local submanifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
PDF BibTeX XML Cite
Full Text: DOI arXiv