Holomorphicity and Walczak formula on Sasakian manifolds

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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 Kähler 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.
15 pages

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Differential Geometry, 53D15, 53D10, 53C56, 53C12, 58E20

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http://salesiana.dossiersoluciones.com/handle/123456789/100818

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407276
 http://arxiv.org/abs/math/0407276

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arXiv