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.

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Barman, Ajit; Ünal, Inan

In this paper, we study Riemannian manifolds admitting a type of semi-symmetric nonmetric connection. By taking the characteristic vector field of this connection as a parallel vector field via the Levi-Civita connection, we examine some curvature properties of Riemannian manifolds. We discuss Ricci-semi symmetry and we consider the conformal curvature tensor. Finally, we study hypersurfaces of Riemanninan manifolds admitting a type of semi-symmetric non-metric connection with a parallel characteristic vector field. We take an example of a Riemannian manifold and we apply our results.

İncele

Barman, Ajit; Ünal, İnan

The object of this paper is to study Kenmotsu manifolds admitting Z−tensor, which is a generalization of Einstein tensor that comes from general rel-ativity. We define a special type of quarter-symmetric non-metric ϕ and η-connection on a Kenmotsu manifold and we examine some geometric properties of such manifolds with Z−tensor. Some semi-symmetry conditions related to Z−tensor are studied on Kenmotsu manifolds and finally, we ob-serve our results on a 5-dimensional Kenmotsu manifold.

AtıfScopus6

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