∗−Conformal η−Ricci Solitons on α−Cosymplectic Manifolds

Abstract

The object of this paper is to study ∗−conformal η−Ricci solitons on α−cosymplectic manifolds. First, α−cosymplectic manifolds admitting ∗−conformal η−Ricci solitons satisfying the conditions R(ξ, .) · S and S(ξ, .) · R = 0 are being studied. Further, α−cosymplectic manifolds admitting ∗−conformal η−Ricci solitons satisfying certain conditions on the M−projective curvature tensor are being considered and obtained several interesting results. Among others it is proved that a φ − M−projeectively semisymmetric α−cosymplectic manifold admitting a ∗−conformal η−Ricci soliton is an Einstein manifold. Finally, the existence of ∗−conformal η−Ricci soliton in an α−cosymplectic manifolds has been proved by a concrete example.