Curvature Properties of Normal Complex Contact metric Manifolds

TL;DR

This paper investigates the curvature properties of normal complex contact metric manifolds, deriving general curvature tensor expressions, conditions for normality, and inequalities related to Ricci curvature.

Contribution

It provides new curvature tensor formulas, necessary and sufficient conditions for normality, and Ricci curvature inequalities for these manifolds.

Findings

Derived general expression of the curvature tensor field.

Established necessary and sufficient conditions for normality.

Presented new inequalities for Ricci curvature.

Abstract

In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold. Also, we give some new equailities for Ricci curvature of normal complex contact metric manifolds.