The Critical Point Equation on Kenmotsu and almost Kenmotsu manifolds

Dhriti Sundar Patra; Amalendu Ghosh; Arindam Bhattacharyya

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arXiv · 1812.03422

The Critical Point Equation on Kenmotsu and almost Kenmotsu manifolds

Dhriti Sundar Patra·Amalendu Ghosh·Arindam Bhattacharyya

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Abstract

In this paper, we have studied the critical point equation (shortly, CPE) within the frame-work of Kenmotsu and almost Kenmotsu manifold satisfying certain nullity conditions. First, we prove that a complete Kenmotsu metric satisfies the CPE is Einstein and locally isometric to the hyperbolic space H2n+1. In case of Kenmotsu manifolds, it is possible to determine the potential function explicitly (locally). We also provide some examples of Kenmotsu and almost Kenmotsu manifolds that satisfies the CPE.

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BibTeX RIS

Dhriti Sundar Patra, Amalendu Ghosh, Arindam Bhattacharyya. 2018-12-09. The Critical Point Equation on Kenmotsu and almost Kenmotsu manifolds. https://arxiv.org/abs/1812.03422

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