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On a class of complete non-compact gradient Yamabe solitons

Jia-Yong Wu
대한수학회 (The Korean Mathematical Society)|2018.05|대한수학회보 (Bulletin of the KMS)|제55권 제3호|pp. 851-863

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키워드

Yamabe solitonfinite topological typeYamabe flowself-similar solution
주제분류수학

초록

We derive lower bounds of the scalar curvature on complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that potential functions of Yamabe solitons have at most quadratic growth for distance function. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.

Abstract

We derive lower bounds of the scalar curvature on complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that potential functions of Yamabe solitons have at most quadratic growth for distance function. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.

참고문헌 (20)

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