On f-non-parabolic ends for Ricci-harmonic metrics

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• 作者：Lin Feng Wang
• 关键词：Ricci ; harmonic metric ; Harmonic Einstein metric ; Scalar curvature ; Structure theorem ; Potential function ; f ; non ; parabolic ; End ; Connectivity
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：51
• 期：1
• 页码：91-107
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Statistics for Business/Economics/Mathematical Finance/Insurance; Theoretical, Mathematical and Computational Physics; Group Theory and Generalizations; Geometry;
• 出版者：Springer Netherlands
• ISSN：1572-9060
• 卷排序：51

文摘

In this paper, we study gradient Ricci-harmonic soliton metrics and quasi Ricci-harmonic metrics (both metrics are called Ricci-harmonic). First, we prove that all ends of \(\tau \)-quasi Ricci-harmonic metrics with \(\tau >1\) should be f-non-parabolic if \(\lambda =0,\mu >0\), or \(\lambda <0, \mu \ge 0\). For the case that \(\lambda<0, \mu < 0\), we can also arrive at the f-non-parabolic property if we add a condition about the scalar curvature. Furthermore, we discuss the connectivity at infinity for quasi Ricci-harmonic metrics. We also conclude that all ends of steady or expanding gradient Ricci-harmonic solitons should be f-non-parabolic, based on which we establish structure theorems for these two solitons.