Quasi Bi-Slant Submanifolds of Nearly Kaehler Manifolds

Abstract

We introduce the notion of quasi bi-slant submanifolds of nearly Kaehler manifolds and study some of thier properties. The necessary and sufficient conditions for the integrability of distributions, involved in the definition of quasi bi-slant submanifolds of nearly Kaehler manifolds, are obtained. We also investigate the necessary and sufficient conditions for quasi bi-slant submanifolds of nearly Kaehler
manifolds to be totally geodesic, and we study the geometry of foliations. Finally, we construct some non-trivial examples of quasi bi-slant manifolds of nearly Kaehler manifolds.

Key words and phrases. Nearly Kaehler manifolds, Quasi bi-slant submanifold, Totally geodesic submanifolds, Totally umbilical submanifolds.

2010 Mathematics Subject Classification. 53B35, 53C15, 53C55