∗-Ricci tensor on (κ,μ)-contact manifolds

Abstract

We introduce the notion of semi-symmetric ∗-Ricci tensor and illustrate that a non-Sasakian (κ,μ)-contact manifold is ∗-Ricci semi-symmetric or has parallel ∗-Ricci operator if and only if it is ∗-Ricci flat. Then we find that among the non-Sasakian (κ,μ)-contact manifolds with the same Boeckx invariant IM, only one is ∗-Ricci flat, so we can think of it as the representative of such class. We also give two methods to construct ∗-Ricci flat (κ,μ)-contact manifolds.

Keywords

• ∗-ricci flat
• ∗-ricci semi-symmetric
• parallel ∗-ricci operator
• (κ
• μ)-contact manifolds