MMN-2905

# Certain results on Kenmotsu pseudo-metric manifolds

• Devaraja Mallesha Naik, Department of Mathematics, Kuvempu University, devarajamaths@gmail.com
• D.G. Prakasha, Department of Mathematics, Karnatak University, prakashadg@gmail.com
• . Venkatesha, Kuvempu University, Department of Mathematics, vensmath@gmail.com

## Abstract

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds is introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature and proved the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of $dim>3$ admitting a Ricci soliton is Einsteinian, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.

Vol. 20 (2019), No. 2, pp. 1083-1099
DOI: 10.18514/MMN.2019.2905