Some remarks on Yamabe solitons
Differential Geometry
2018-03-15 v1
Abstract
In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold 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.
Keywords
Cite
@article{arxiv.1803.05204,
title = {Some remarks on Yamabe solitons},
author = {Debabrata Chakraborty and Yadab Chandra Mandal and Shyamal Kumar Hui},
journal= {arXiv preprint arXiv:1803.05204},
year = {2018}
}
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5 pages