Biharmonic holomorphic maps and conformally Kahler geometry

Details Biharmonic holomorphic maps and conformally Kahler geometry Biharmonic holomorphic maps and conformally Kahler geometry

2012-04-10

arxiv.org/abs/1204.2104v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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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