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arXiv · 1711.07623

Complete Yamabe solitons with finite total scalar curvature

Shun Maeta
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Abstract

In this paper, we show that steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive Ricci curvature are Ricci flat. Moreover, under certain pinching condition for Ricci curvature, we show that steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive scalar curvature have zero scalar curvature.

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Shun Maeta. 2017-11-21. Complete Yamabe solitons with finite total scalar curvature. https://arxiv.org/abs/1711.07623

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