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<p>The well-known Berwald square metric is a positively complete and projectively flat Finsler metric with vanishing flag curvature. In this paper, we study a positively complete square metric on a manifold. We show a rigidity result that if the Ricci curvature is constant, then it must be isometric to the Berwald square metric. This is not true without assumption on the completeness of the metric.</p>

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On Positively Complete Einstein Square Metrics

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Zhongmin Shen,
  • Hongmei Zhu

摘要

The well-known Berwald square metric is a positively complete and projectively flat Finsler metric with vanishing flag curvature. In this paper, we study a positively complete square metric on a manifold. We show a rigidity result that if the Ricci curvature is constant, then it must be isometric to the Berwald square metric. This is not true without assumption on the completeness of the metric.