On CR-structures and F-structure satisfying FK + (-)K+1F=0

CR-submanifolds of a Kahlerian manifold have been defined by Bejancu [1], and are now being studied by various authors, see [2, 3, 9]. The theory of f-structure was developed by Yano [7], Yano and Ishihara [8]. Goldberg [5] and others. The purpose of this paper is to show a relationship between CR-structures and F-structure satisfying F-K + (-)(K+1) F = 0, F-W + (-)(W+1) F not equal 0, for 1 < W < K, where K is a fixed positive integer greater than 2. The case when k is odd (>= 3) has been considered in this paper.