On the Frobenius integrability of certain holomorphic \(p\)-forms. (English) Zbl 1011.32019

Bauer, Ingrid (ed.) et al., Complex geometry. Collection of papers dedicated to Hans Grauert on the occasion of his 70th birthday. Berlin: Springer. 93-98 (2002).
Summary: The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic \(p\)-forms with values in certain line bundles with semi-negative curvature on a compact Kähler manifold. There are in fact very strong restrictions, both on the holomorphic form and on the curvature of the semi-negative line bundle. In particular, these observations provide interesting information on the structure of projective manifolds which admit a contact structure: either they are Fano manifolds or, thanks to results of Kebekus-Peternell-Sommese-Wisniewski, they are biholomorphic to the projectivization of the cotangent bundle of another suitable projective manifold.
For the entire collection see [Zbl 0989.00069].


32Q15 Kähler manifolds
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
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