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Critical metrics with cyclic parallel Ricci tensor for volume functional on manifolds with boundary

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Abstract

In this paper, we study the critical metrics with cyclic parallel Ricci tensor for volume functional on manifolds with boundary. We show such metric is isometric to a geodesic ball in a simply connected space form \(\mathbb {R}^n\), \(\mathbb {H}^n\) or \(\mathbb {S}^n\) under some extra conditions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Weimin Sheng & Lisheng Wang

Authors
  1. Weimin Sheng
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  2. Lisheng Wang
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Correspondence to Weimin Sheng.

Additional information

The authors were supported by NSF in China No. 11571304.

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Sheng, W., Wang, L. Critical metrics with cyclic parallel Ricci tensor for volume functional on manifolds with boundary. Geom Dedicata 201, 243–251 (2019). https://doi.org/10.1007/s10711-018-0391-9

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  • DOI: https://doi.org/10.1007/s10711-018-0391-9

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