Holomorphic Isometries on Complex Finsler Manifolds

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• 作者：Rongmu Yan
• 关键词：Complex Finsler manifold ; Holomorphic isometry ; Complex homogeneous manifold ; Holomorphic Killing vector field
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：26
• 期：2
• 页码：1269-1279
• 全文大小：396 KB
• 参考文献：1.Abate, M., Patrizio, G.: Finsler Metric—A Global Approach, Lecture Notes in Mathematics, vol. 1591. Springer, Berlin (1994)MATH
  2.Bao, D., Chern, S.S., Shen, Z.: An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, vol. 200. Springer, New York (2000)CrossRef
  3.Deng, S., Hou, Z.: Invariant Finsler metrics on homogeneous manifolds: II complex structures. J. Phys. A. 39, 2599–2609 (2006)MathSciNet CrossRef MATH
  4.Helgason, S.: Differential Geometry Lie groups and Symmetric Spaces. Academic Press, New York (1978)MATH
  5.Kobayashi, S.: Fixed points of isometries. Nagoya Math. J. 13, 63–68 (1958)MathSciNet MATH
  6.Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, vol. I, II. Interscience, New York (1963)MATH
  7.Ozols, V.: Critical points of the displacement function of an isometry. J. Diff. Geom. 3, 411–432 (1969)MathSciNet MATH
  8.Yan, R.: On the volume of the projectivized tangent bundle in a complex Finsler manifold. Arch. Math. 86, 458–463 (2006)MathSciNet CrossRef MATH
  
• 作者单位：Rongmu Yan (1)
  
  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

This paper gives a geometric description of the critical points of the displacement function of a holomorphic isometry for complex Finsler manifolds. It also considers the 1-real parameter group of holomorphic isometries and obtains some rigid results.