Ünal, İnan; Barman, Ajit; Prakasha, D.G.

This chapter explores Chen-Ricci inequalities for submanifolds of Kenmotsu space forms endowed with a ϕ−η-connection, a special type of quarter-symmetric metric connection. The geometric background of Kenmotsu space forms and the properties of the ϕ−η-connection are briefly introduced, followed by the derivation of relevant curvature relations. The study proceeds by examining submanifolds within this framework, focusing on the behavior of curvature tensors and associated Riemannian invariants. Using the properties of the ambient space and the chosen connection, several inequalities involving Chen invariants and Ricci curvatures are obtained.

İncele

Prakasha, D.G.; Deepika, M.V.; Ünal, İnan

In this study, we investigate Lorentzian para-Kenmotsu (LP-Kenmotsu (LPK)) manifolds in the context of the generalized Tanaka-Webster connection, denoted as D*. Initially, we derive the formulas for the curvature tensor, Ricci tensor, and scalar curvature of an LPK manifold with respect to the connection D*. We analyze the geometric properties of these manifolds, including their local symmetry, Ricci semi-symmetry, and local ψ-symmetry. Furthermore, utilizing the Q-curvature tensor, we analyze conditions under which LPK manifolds exhibit Q*-flatness, Q*-Ricci semi-symmetry, and ψ-Q*-flatness concerning the connection D*.

İncele

Una, I.; Sarı, R.; Prakasha, D.G.

In this paper we study NMCP manifolds, which are (2p+2q+2)−dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the ⋆−Ricci tensor. We prove that a⋆−Ricci-semi-symmetric NMCP manifold is ⋆−Ricci-flat, and that a ⋆−generalized quasi-Einstein NMCP manifold cannot be ⋆−Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space

AtıfScopus1

İncele

Amruthalakshmi, M.R.; Prakasha, D.G.; Bin Turki, Nasser; Unal, Inan

In this paper, we study α-cosymplectic manifold M admitting ∗-Ricci tensor. First, it is shown that a ∗-Ricci semisymmetric manifold M is ∗-Ricci flat and a φ-conformally flat manifold M is an η-Einstein manifold. Furthermore, the ∗-Weyl curvature tensor W∗ on M has been considered. Particularly, we show that a manifold M with vanishing ∗-Weyl curvature tensor is a weak φ-Einstein and a manifold M fulfilling the condition RE1,E2⋅W∗=0 is η-Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold M admitting ∗-Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting ∗-Ricci soliton and almost ∗-Ricci soliton are drawn.

AtıfScopus5·OpenAlex5

İncele