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

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Abstract

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.

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Authors and Affiliations

  1. School of Science, Nantong University, Nantong, 226007, China

    Lin Feng Wang

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  1. Lin Feng Wang
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Correspondence to Lin Feng Wang.

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The author was supported in part by the NSF of Jiangsu Province (BK20141235).

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Wang, L.F. On f-non-parabolic ends for Ricci-harmonic metrics. Ann Glob Anal Geom 51, 91–107 (2017). https://doi.org/10.1007/s10455-016-9525-1

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  • DOI: https://doi.org/10.1007/s10455-016-9525-1

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