Some Characterizations for Kenmotsu Manifolds Admitting a General Connection

Abstract

In this paper, we discuss η-Ricci solitons on Kenmotsu manifolds. While investigating η-Ricci solitons, we consider η-Ricci soliton in Kenmotsu manifold with respect to a general connection instead of the Levi-Civita connection. We present the geometry of Kenmotsu manifolds admitting a general connection under the conditions of Ricci pseudosymmetry and Ricci semisymmetry. Using the general connection, we obtain the characterizations of Ricci pseudosymmetric and Ricci semisymmetric Kenmotsu manifolds with respect to quarter-symmetric connection, Schouten-Van Kampen connection, Tanaka-Webster connection, and Zamkovoy connection.