Holomorphicity and Walczak formula on Sasakian manifolds

Details Holomorphicity and Walczak formula on Sasakian manifolds Holomorphicity and Walczak formula on Sasakian manifolds

2004-07-15

arxiv.org/abs/math/0407276v3

Mathematics

Differential Geometry

15 pages

Scientific paper

Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are dealing with K\"ahler manifolds and holomorphic (integrable) distributions. Here, with adapted notions as invariant distribution and (contact) holomorphicity, we derive the special form of the Walczack formula on a Sasaki manifold. Then we apply a standard Bochner argument in the study of (contact) holomorphic distributions. Some other applications for (pseudo)harmonic morphisms on a Sasaki manifolds are outlined.

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