Curve Theory in Extended Manifold

Abstract

A structure is almost complex structure if $J^2=-I, I$ over a complex manifold $M$, where $J$ is a tensor field of type (1,1) and $I$ is the identity tensor field. Now let us consider that $^kExtendd ManifoldComplex ManifoldM$ is the extended complex manifold of manifold $M$. The order of extended complex manifold is $k$. On extended complex manifold $^kM$, extended almost complex structure satisfies condition $(J_k)^2=-I$. In this paper we study some properties of various lifts on extended complex structure on an extended complex manifold $^kM$. We define and study various properties of the submanifold $^kV$ of extended complex manifold $^kM$. Further we elaborated the conditions of existing distributions of real dimensions of extended complex manifold $^kM$. In the last we define Haantje's tensor on extended complex manifold $^kM$.