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