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

摘要

In the present paper, we study hemi-slant submanifolds of a locally productRiemannian manifold. We prove that the anti-invariant distribution which isinvolved in the definition of hemi-slant submanifold is integrable and givesome applications of this result. We get a necessary and sufficient conditionfor a proper hemi-slant submanifold to be a hemi-slant product. We also studythis type submanifolds with parallel canonical structures. Moreover, we givetwo characterization theorems for the totally umbilical proper hemi-slantsubmanifolds. Finally, we obtain a basic inequality involving Ricci curvatureand the squared mean curvature of a hemi-slant submanifold of a certain typelocally product Riemannian manifold.