Global Conharmonic Concept Type Nearly Kahler Manifold

Abstract

The concept of permanence conharmonic type Nearly Kahler manifold conditions are obtained when the Nearly Kahler manifold is a manifold conharmonic constant type. Proved that the local conharmonic constancy of type Nearly Kahler manifold is equivalent to its global conharmonic constancy of type. And also proved that the Nearly Kahler manifold conharmonic constant type is a manifold of constant scalar curvature.
The notion of constancy of type Nearly Kahler manifolds was introduced A.Greem ([1], [2], [3]) and has proved very useful in the study of the geometry of nearly kahler manifolds. Next nearly kahler manifolds of constant type considered various mathematicians (see. [1], [3], [4], [5], [6], [7]). Comprehensive description of Nearly Kahler manifolds of constant type was obtained V.F.Kirichenko [6]. In [6] it is shown that Nearly Kahler manifold of pointwise constant type description by the identity  , where B - a function on Nearly Kahler manifold, . Wherein local constancy of type Nearly Kahler manifold is equivalent to the local constancy of its type. Moreover, the covariant constancy of structure tensors of the first and second kind it follows immediately that, the constancy of type at only one point Nearly Kahler space implies global consistency of its type.