Science China Mathematics

, Volume 61, Issue 3, pp 535–544 | Cite as

Strongly convex weakly complex Berwald metrics and real Landsberg metrics

  • Yong He
  • Chunping Zhong


Under the assumption that F is a strongly convex weakly Kähler Finsler metric on a complex manifold M, we prove that F is a weakly complex Berwald metric if and only if F is a real Landsberg metric. This result together with Zhong (2011) implies that among the strongly convex weakly Kähler Finsler metrics there does not exist unicorn metric in the sense of Bao (2007). We also give an explicit example of strongly convex Kähler Finsler metric which is simultaneously a complex Berwald metric, a complex Landsberg metric, a real Berwald metric, and a real Landsberg metric.


strongly convex Kähler Finsler metric Kähler Finsler metric real Landsberg metric real Berwald metric 


53C60 53C40 


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This work was supported by Program for New Century Excellent Talents in University (Grant No. NCET-13-0510), National Natural Science Foundation of China (Grant Nos. 11271304, 10971170, 11171277, 11571288, 11461064 and 11671330), the Fujian Province Natural Science Funds for Distinguished Young Scholar (Grant No. 2013J06001) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.


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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.School of Mathematical SciencesXinjiang Normal UniversityUrumqiChina

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