ALMOST CONTACT METRIC STRUCTURE ON AN ODD DIMENSIONAL SPHERE

ABSTRACT Parallel fields of planes were used by Patterson (1953) to characterize Kaehler manifolds, and Sasaki (1960) predicted differentiable manifolds having specific structures that are intimately associated with almost contact structures. Additionally, the conformal symmetric tensor of Kaehlerian manifolds was discussed by Negi and Sulochana (2021). We obtained an almost contact metric structure on an odd dimensional sphere in this article. Again, we discover the submanifold of the virtually contact metric manifold in the metric compound structure and the odd-dimensional sphere. Keywords: Riemannian manifold, almost contact manifold, Sasakian manifold, almost complex manifold, Nijenhuis tensors.