Complete Hypersurfaces of Constant Isotropic Curvature in Space Forms

H. A. Gururaja; Niteesh Kumar

Complete Hypersurfaces of Constant Isotropic Curvature in Space Forms

Differential Geometry 2022-10-18 v2

Authors: H. A. Gururaja , Niteesh Kumar

Abstract

We classify complete orientable hypersurfaces of constant isotropic curvature in space forms. We show that such a hypersurface has constant mean curvature only if it is an isoparametric hypersurface, and that it is minimal if and only if it is totally geodesic or it is the Clifford minimal hypersurface ${\mathbb S}^{3}(\frac{4c}{3})\times {\mathbb S}^{1}(4c)$ in ${\mathbb S}^{5}(c).$

Keywords

complete hypersurfaces constant isotropic curvature space forms constant mean curvature isoparametric hypersurfaces clifford minimal hypersurface

Cite

@article{arxiv.2206.15120,
  title  = {Complete Hypersurfaces of Constant Isotropic Curvature in Space Forms},
  author = {H. A. Gururaja and Niteesh Kumar},
  journal= {arXiv preprint arXiv:2206.15120},
  year   = {2022}
}

Comments

12 Pages. Minor errors have been corrected and new examples are added

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