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arXiv · 1204.2104

Biharmonic holomorphic maps and conformally Kahler geometry

M. Benyounes·E. Loubeau·R. Slobodeanu
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Abstract

We give conditions on the Lee vector field of an almost Hermitian manifold such that any holomorphic map from this manifold into a (1,2)-symplectic manifold must satisfy the fourth-order condition of being biharmonic, hence generalizing the Lichnerowicz theorem on harmonic maps. These third-order non-linear conditions are shown to greatly simplify on l.c.K. manifolds and construction methods and examples are given in all dimensions.

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M. Benyounes, E. Loubeau, R. Slobodeanu. 2012-04-10. Biharmonic holomorphic maps and conformally Kahler geometry. https://arxiv.org/abs/1204.2104

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