International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 3, Pages 167-172
doi:10.1155/S0161171201005257
Submanifolds of F-structure manifold satisfying FK+(−)K+1F=0
Department of Mathematics and Computer Science, Kent State University, Tuscarawas Campus, New Philadelphia 44663, OH, USA
Received 2 May 2000
Copyright © 2001 Lovejoy S. Das. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The purpose of this paper is to study invariant submanifolds of an n-dimensional manifold M endowed with an F-structure satisfying FK+(−)K+1F=0 and FW+(−)W+1F≠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. We show that an invariant submanifold M˜, embedded in an F-structure manifold M in such a way that the complementary distribution Dm is never tangential to the invariant submanifold ψ(M˜), is an almost complex manifold with the induced F˜-structure. Some theorems regarding the integrability conditions of induced F˜-structure are proved.