The Hermitian Connection and the Jacobi Fields of a Complex Finsler Manifold

Details The Hermitian Connection and the Jacobi Fields of a Complex Finsler Manifold The Hermitian Connection and the Jacobi Fields of a Complex Finsler Manifold

2000-09-07

arxiv.org/abs/math/0009067v1

Mathematics

Differential Geometry

Scientific paper

It is proved that all invariant functions of a complex Finsler manifold can
be totally recovered from the torsion and curvature of the connection
introduced by Kobayashi for holomorphic vector bundles with complex Finsler
structures. Equations of the geodesics and Jacobi fields of a generic complex
Finsler manifold, expressed by means Kobayashi's connection, are also derived.

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