Abstract

In this paper, we examine a submanifold $N$ of an $\alpha$-cosymplectic manifold equipped with a torqued vector field $\tau$. We also investigate submanifolds that admit a $*$-$\eta$-Ricci soliton within the framework of $\alpha$-cosymplectic manifolds with torqued vector field $\tau$. We establish the necessary conditions for such a submanifold to reduce to a simpler form and demonstrate that the tangential component of $\tau$ acts as a torse-forming vector field on $N$. Finally, we present an example of a 3-dimensional submanifold of a 5-dimensional $\alpha$-cosymplectic manifold which verifies our results.

Keywords and Phrases

$\alpha$-cosymplectic manifold, $*$-$\eta$-Ricci soliton, Torqued vector field.

A.M.S. subject classification

53C15, 53C25, 53C17, 53D15, 53D10.

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