• Korean Journal of Mathematics
• /
• v.29 no.4
• /
• pp.705-714
• /
• 2021

In the present paper, we study 𝜂-Ricci solitons on para-Kenmotsu manifolds with Codazzi type of the Ricci tensor. We study 𝜂-Ricci solitons on para-Kenmotsu manifolds with cyclic parallel Ricci tensor. We also study 𝜂-Ricci solitons on 𝜑-conformally semi-symmetric, 𝜑-Ricci symmetric and conformally Ricci semi-symmetric para-Kenmotsu manifolds. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits 𝜂-Ricci solitons.

• Journal of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.435-445
• /
• 2005

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

• Honam Mathematical Journal
• /
• v.42 no.2
• /
• pp.331-344
• /
• 2020

The objective of the present paper is to study certain curvature conditions in Kenmotsu manifolds with respect to the semi-symmetric non-metric connection. Finally, we construct an example of 5-dimensional Kenmotsu manifold with respect to the semi-symmetric non-metric connection to verify some results of the paper.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.3
• /
• pp.281-293
• /
• 2019

In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian ${\beta}$-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.613-626
• /
• 2021

The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of three-dimensional Ricci symmetric and 𝜂-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1259-1280
• /
• 2016

The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.