Submanifold of extended complex manifold

Abstract

The present paper is study to investigate some properties of various lifts on an extended complex structure defined over extended complex manifold $^kM$. We define the submanifold $^kV$ of an extended complex manifold $^kM$ and obtain fundamental results of it. Further, we elaborated the conditions of existing distributions of real dimensions of an extended complex manifold $^kM$. In the last, we define Haantje's tensor on $^kM$ and discuss various properties of it.