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arXiv · 1908.00334

Non-existence of Riemannian metric satisfying Yamabe soliton

Absos Ali Shaikh·Chandan Kumar Mondal
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Abstract

In this paper we have proved that a compact Riemannian manifold does not admit a metric with positive scalar curvature if there exists a real valued function in this manifold which is strictly positive along a geodesic ray satisfying expanding or steady Yamabe soliton. We have also deduced a relation between scalar curvature and surface area of a geodesic ball in a Riemannian manifold with a pole satisfying steady Yamabe soliton.

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Absos Ali Shaikh, Chandan Kumar Mondal. 2019-08-01. Non-existence of Riemannian metric satisfying Yamabe soliton. https://arxiv.org/abs/1908.00334

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