Cohomology of semi-invariant submanifolds of cosymplectic manifolds

Abstract

In this paper, we study de Rham cohomology class for semi-invariant submanifolds of a cosymplectic manifold. We show that there are de Rham cohomolgy class on semi-invariant submanifold of a cosymplectic manifold. Firstly, we define semi-invariant submanifolds of a cosyplectic manifold. We present an example for semi-invariant submanifold of a cosymplectic manifold.Later, We obtain characterizations, investigate the geometry of distributions which arise from the definition of semi-invariant submanifold. We obtain that invariant distribtion is always integrable and minimal. Moreover, necessary and sufficient conditions investigate for the anti-invariant distribution to be integrable and minimal. Finally, we prove that semiinvariant submanifold of a cosymplectic manifold has nontrivial de Rham cohomology class. Further, the theoretical methodology of mathematics are used to obtain results.