The index of a holomorphic mapping and the index theorem

Ishihara, Tôru

doi:10.1090/S0002-9939-1977-0494249-7

The index of a holomorphic mapping and the index theorem
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Proc. Amer. Math. Soc. 66 (1977), 169-174 Request permission

Abstract:

The index theorem for a harmonic mapping of riemannian manifolds is given. Let $f:M \to N$ be a holomorphic mapping of Kaehler manifolds. Then it is shown that the index of f is zero and that a Jacobi field along f is a holomorphic section of the bundle ${f^ \ast }T(N)$ induced by f.

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