Abstract
In this paper, the author establishs a real-valued function on Kähler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete Kähler manifolds, then they are holomorphically isometric.
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References
Ambrose, W., Parallel translation of Riemannian curvature, Annals of Mathematics, 64, 1956, 337–363.
Chen, W. and Li, X., An Introduction to Riemann Geometry, Peking University Press, Beijing, 2004 (in Chinese).
Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces, 2nd ed., Academic Press, New York, San Francisco, London, 1978.
Acknowledgement
The author would like to thank the reviewer for his (her) very careful and valuable comments.
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This work was supported by the National Natural Science Foundation of China (Nos. 11571287, 11871405), the Fundamental Research Funds for the Central Universities (No. 20720150006) and the Natural Science Foundation of Fujian Province of China (No. 2016J01034).
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Yan, R. Parallel Translation on Kähler Manifolds. Chin. Ann. Math. Ser. B 41, 451–464 (2020). https://doi.org/10.1007/s11401-020-0210-0
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DOI: https://doi.org/10.1007/s11401-020-0210-0