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- Title
Splitting theorem for sheaves of holomorphic k-vectors on complex contact manifolds.
- Authors
Moriyama, Takayuki; Nitta, Takashi
- Abstract
A complex contact structure γ is defined by a system of holomorphic local 1-forms satisfying the completely non-integrability condition. The contact structure induces a subbundle Ker γ of the tangent bundle and a line bundle L. In this paper, we prove that the sheaf of holomorphic k -vectors on a complex contact manifold splits into the sum of 𝒪 (∧ k Ker γ) and 𝒪 (L ⊗ ∧ k − 1 Ker γ) as sheaves of ℂ -module. The theorem induces the short exact sequence of cohomology of holomorphic k -vectors, and we obtain vanishing theorems for the cohomology of 𝒪 (∧ k Ker γ).
- Subjects
SHEAF theory; HOLOMORPHIC functions; SHEAF cohomology; CONTACT manifolds; COHOMOLOGY theory; TANGENT bundles; VECTOR bundles; VANISHING theorems
- Publication
International Journal of Mathematics, 2018, Vol 29, Issue 13, pN.PAG
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X1850091X