Holomorphicity and the Walczak formula on Sasakian manifolds

[摘要] The Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. M. Svensson [Holomorphic foliations, harmonic morphisms and the Walczak formula, J. London Math. Soc. (2) 68 (3) (2003) 781-794] has shown that this formula simplifies to a Bochner-type formula when we are dealing with Kahler manifolds and holomorphic (integrable) distributions. We show in this paper that such results have a counterpart in Sasakian geometry. To this end, we build on a theory of (contact) holomorphicity on almost contact metric manifolds. Some other applications for (pseudo-)harmonic morphisms on Sasaki manifolds are outlined. (c) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-31

[关键词] (almost) contact manifolds;Sasakian manifolds;distribution;holomorphicity