2004/07/15 by Vasile Brinzanescu, Vasile Brînzănescu, Brinzanescu, Vasile +2
Mathematics · #53C12 #53C56 #53D10 #53D15 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG #msc:53C12 #msc:53C56 #msc:53D10 #msc:53D15 #msc:58E20
paper · pdf · doi:10.48550/arxiv.math/0407276
15 pages
openalex publication_date 2004/07/15 · arxiv created 2006/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.