Invariants of a Complex Cotangent Line Field
by
Sidney Webster
Vol. 8 No. 2 (2013) P.259~P.267
ABSTRACT
We study a complex manifold $M$ together
with a smooth complex line sub-bundle $E$ of its (1,0)-cotangent bundle. $E$ is assumed to satisfy a certain integrability condition and a non-degeneracy condition. We attach to the structure $(M,E)$ an invariant generalized connection on a principal bundle $P$ over $M$ of adapted coframes. The total space of $E$ minus its zero section has a natural almost complex structure. We determine when it is actually a complex structure.
KEYWORDS
$\delta$-integrability, non-degenerate Levi-form, biholomorphic invariants.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32V40, 32N05
MILESTONES
Received: 2012-09-01
Revised : 2012-12-10
Accepted: 2012-12-10
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