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arXiv · 1908.00691

Rigid properties of generalized $\tau$-quasi Ricci-harmonic metrics

Fanqi Zeng
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Abstract

In this paper, we study compact generalized $\tau$-quasi Ricci-harmonic metrics. In the first part, we explore conditions under which generalized $\tau$-quasi Ricci-harmonic metrics are harmonic-Einstein and give some characterization results for it. In the second part, we obtain some rigidity results for compact $(\tau, \rho)$-quasi Ricci-harmonic metrics which are special case of generalized $\tau$-quasi Ricci-harmonic metrics. In the third part, we shall give two gap theorems for compact $\tau$-quasi Ricci-harmonic metrics by showing some necessary and sufficient conditions for the metrics to be harmonic-Einstein.

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Fanqi Zeng. 2019-08-02. Rigid properties of generalized $\tau$-quasi Ricci-harmonic metrics. https://arxiv.org/abs/1908.00691

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