Parallel Translation on Kähler Manifolds

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.

Keywords

Kähler manifold / Holomorphic sectional curvature / Parallel translation

References

[1] Ambrose W. Parallel translation of Riemannian curvature. Annals of Mathematics, 1956, 64: 337-363

[2] Chen W, Li X. An Introduction to Riemann Geometry, 2004, Beijing: Peking University Press

[3] Helgason S. Differential Geometry. Lie Groups and Symmetric Spaces, 1978 2nd Academic Press: New York, San Francisco, London