Immersion of the Ricci-recurrent normal almost contact metric manifolds

Abstract

In this paper, we investigate the immersion of three-dimensional Ricci-recurrent normal almost contact metric manifolds into four-dimensional Riemannian manifolds with constant curvature 1. A relationship between the shape operator A and the structure tensor defining the normal almost contact structure is derived. We explore the geometric implications of structure tensor under specific conditions and establish connections between the scalar functions connected with the almost normal contact metric manifold that are associated with the covariant derivative of the Reeb vector field. Additionally, the study characterizes the behavior of the vector field associated with the Ricci-recurrence 1-form, emphasizing its impact on the manifold's curvature and immersion properties.