Projective Curvature Tensor on N($\kappa$)-Contact Metric Manifold Admitting Semi-Symmetric Non-Metric Connection

Abstract

The object of the present paper is to classify $N(\kappa)$-contact metric manifolds admitting the semi-symmetric non-metric connection with certain curvature conditions the projectively curvature tensor. We studied projective flat, $\xi- $projectively flat, $\phi- $projectively flat $N(\kappa )$-contact metric manifolds admitting the semi-symmetric non-metric connection. Also, we examine such manifolds under some local symmetry conditions related to projective curvature tensor.

Keywords

• $N(\kappa)$-contact metric manifolds
• Projective curvature tensor
• Semi-symmetric non-metric connection

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