Some Results About Concircular and Concurrent Vector Fields On Pseudo-Kaehler Manifolds

Abstract

Kaehler manifolds which are used in physics have a lot of application fields. In this study we only state concircular and concurrent vector field that are defined on these manifolds. A vector field on a pseudo-Riemannian manifold N is called concircular, if it satisfies ∇Xυ = μX for any vector X tangent to N, where ∇ is the Levi-Civita connection of N. Furthermore, a concircular vector field υ is called a concurrent vector field if the function μ is non-constant. So, we provide some results on submanifolds of pseudo-Kaehler manifolds with respect to a concircular vector field or a concurrent vector field. Morever, we investigate this problem for another manifolds and proof some theorems.