Quaternionic connections, induced holomorphic structures and a vanishing theorem

Details Quaternionic connections, induced holomorphic structures and a vanishing theorem Quaternionic connections, induced holomorphic structures and a vanishing theorem

2006-06-28

arxiv.org/abs/math/0606715v3

Mathematics

Differential Geometry

22 pages

Scientific paper

We classify the holomorphic structures of the tangent vertical bundle T of the twistor fibration of a quaternionic manifold (M,Q) of dimension bigger than four. In particular, we show that any self-dual quaternionic connection on (M, Q) induces an holomorphic structure on T. We prove that the positive tensor powers of T have no global holomorphic sections, when (M,Q) is compact and admits a compatible quaternionic-Kahler metric of negative (respectively, zero) scalar curvature and the holomorphic structure of T is induced by a closed (respectively, closed but not exact) quaternionic connection.

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