On Positively Complete Einstein Square Metrics  

作　　者：Zhongmin Shen Hongmei Zhu 

机构地区：[1]Department of Mathematical Sciences,Indiana University-Purdue University,Indianapolis,46202-3216,USA [2]College of Mathematics and Information Science,He’nan Normal University,Xinxiang,453007,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第3期1015-1022,共8页数学学报(英文版)

基　　金：in part supported by NSFC (Grant No. 11671352);supported by NSFC (Grant No. 11901170)

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.

关 键 词：Finsler metric Einstein square metric Berwald square metric 

分 类 号：O186.1[理学—数学]