Generic Riemannian Maps from Nearly Kaehler Manifolds

Abstract

In order to generalise semi-invariant Riemannian maps, Sahin first introduced the idea of “Generic Riemannian maps”. We extend the idea of generic Riemannian maps to the case in which the total manifold is a nearly Kaehler manifold. We study the integrability conditions for the horizontal distribution although vertical distribution is always integrable. We also study the geometry of foliations of two distributions and obtain the necessary and sufficient condition for generic Riemannian maps to be totally geodesic. Additionally, we study the generic Riemannian map with umbilical fibers.

Keywords

• nearly Kaehler manifold
• Riemannian maps
• generic Riemannian maps
• anti-invariant
• semi-invariant Riemannian maps and product manifolds