Inequalities for algebraic Casorati curvatures and their applications

Mukut Mani Tripathi

Inequalities for algebraic Casorati curvatures and their applications

Differential Geometry 2016-07-21 v1

Authors: Mukut Mani Tripathi

Abstract

The notion of different kind of algebraic Casorati curvatures are introduced. Some results expressing basic Casorati inequalities for algebraic Casorati curvatures are presented. Equality cases are also discussed. As a simple application, basic Casorati inequalities for different $\delta$ -Casorati curvatures for Riemannian submanifolds are presented. Further applying these results, Casorati inequalities for Riemannian submanifolds of real space forms are obtained. Finally, some problems are presented for further studies.

Keywords

algebraic Casorati curvature Casorati inequality Riemannian submanifold real space form differential geometry

Cite

@article{arxiv.1607.05828,
  title  = {Inequalities for algebraic Casorati curvatures and their applications},
  author = {Mukut Mani Tripathi},
  journal= {arXiv preprint arXiv:1607.05828},
  year   = {2016}
}

Comments

Submitted to the Proceedings of ICDG FEZ 2016 to be published in Note di Mat

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