Splitting theorem for sheaves of holomorphic k-vectors on complex contact manifolds

Abstract

A complex contact structure [Formula: see text] is defined by a system of holomorphic local 1-forms satisfying the completely non-integrability condition. The contact structure induces a subbundle [Formula: see text] of the tangent bundle and a line bundle [Formula: see text]. In this paper, we prove that the sheaf of holomorphic [Formula: see text]-vectors on a complex contact manifold splits into the sum of [Formula: see text] and [Formula: see text] as sheaves of [Formula: see text]-module. The theorem induces the short exact sequence of cohomology of holomorphic [Formula: see text]-vectors, and we obtain vanishing theorems for the cohomology of [Formula: see text].