1. The geometry of hemi-slant submanifolds of a locally product Riemannian manifold
- Author
-
Fatma Özdemir and Hakan Mete Taştan
- Subjects
Mathematics - Differential Geometry ,Mean curvature ,Integrable system ,Locally product manifold,hemi-slant submanifold,slant distribution ,General Mathematics ,Mathematics::History and Overview ,Geometry ,Riemannian manifold ,Submanifold ,Computer Science::Computers and Society ,Statistical manifold ,Differential Geometry (math.DG) ,Primary 53B25, Secondary 53C55 ,Product (mathematics) ,Computer Science::Computer Vision and Pattern Recognition ,FOS: Mathematics ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Ricci curvature ,Distribution (differential geometry) ,Mathematics - 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.
- Published
- 2015