The geometry of hemi-slant submanifolds of a locally product Riemannian manifold


Tastan H. M. , Özdemir F.

Turkish Journal of Mathematics, vol.39, no.2, pp.268-284, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.3906/mat-1407-18
  • Title of Journal : Turkish Journal of Mathematics
  • Page Numbers: pp.268-284

Abstract

In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study these types of submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.