Abstract
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.
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Acknowledgments
This is supported by the Natural Science Foundation of Fujian Province of China (2012J01020, 2014J01022).
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Yan, R. Holomorphic Isometries on Complex Finsler Manifolds. J Geom Anal 26, 1269–1279 (2016). https://doi.org/10.1007/s12220-015-9591-9
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DOI: https://doi.org/10.1007/s12220-015-9591-9
Keywords
- Complex Finsler manifold
- Holomorphic isometry
- Complex homogeneous manifold
- Holomorphic Killing vector field