Torse-forming Vector Field and Ricci–Bourguignon Soliton on a Generic Submanifold of a Kenmotsu Manifold

Abstract

The aim of this paper is to derive significant results related to generic submanifolds and the generic product of Kenmotsu manifolds equipped with torse-forming vector fields. In particular, we investigate the existence and non-existence of tangential component u^T of a vector u, which is a torse-forming vector field on D^T, the invariant distribution of a generic submanifold N.
Additionally, we establish necessary and sufficient condition for a submanifold of a Kenmotsu manifold to be umbilical. Furthermore, we present the necessary and sufficient conditions for D^T and D^⊥, representing the invariant and anti-invariant distributions of a generic submanifold admitting a Ricciourguignon soliton to be Einstein. Lastly, we illustrate a 5-dimensional generic submanifold within a 7-dimensional Kenmotsu manifold through an example.

Keywords: Generic submanifold; Torse-forming vector field; Ricci–Bourguignon soliton.

2010 Mathematics Subject Classification. 53C15; 53C25; 53D15