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arXiv · 1803.05204

Some remarks on Yamabe solitons

Debabrata Chakraborty·Yadab Chandra Mandal·Shyamal Kumar Hui
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Abstract

In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold $M^n$ when the metric is a Yamabe soliton. Using these quantities we have obtained bound on the soliton constant. We have proved that the commutator of two soliton vector fields with the same metric in a given conformal class produces a Killing vector field. Also it is shown that the soliton vector field becomes a geodesic vector field if and only if the manifold is of constant curvature.

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Debabrata Chakraborty, Yadab Chandra Mandal, Shyamal Kumar Hui. 2018-03-14. Some remarks on Yamabe solitons. https://arxiv.org/abs/1803.05204

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