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arXiv · 1711.05935

The Critical Point Equation And Contact Geometry

Amalendu Ghosh·Dhriti Sundar Patra
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Abstract

In this paper, we consider the CPE conjecture in the frame-work of $K$-contact and $(\kappa, \mu)$-contact manifolds. First, we prove that if a complete $K$-contact metric satisfies the CPE is Einstein and is isometric to a unit sphere $S^{2n+1}$. Next, we prove that if a non-Sasakian $ (\kappa, \mu) $-contact metric satisfies the CPE, then $ M^{3} $ is flat and for $ n > 1 $, $ M^{2n+1} $ is locally isometric to $ E^{n+1}\times S^{n}(4)$.

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Amalendu Ghosh, Dhriti Sundar Patra. 2017-11-16. The Critical Point Equation And Contact Geometry. https://doi.org/10.1007/s00022-016-0333-3

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