About the geometry of almost para-quaternionic manifolds

Details About the geometry of almost para-quaternionic manifolds About the geometry of almost para-quaternionic manifolds

2008-08-07

arxiv.org/abs/0808.1046v2

Mathematics

Differential Geometry

26 pages

Scientific paper

We provide a general criteria for the integrability of the almost para-quaternionic structure of an almost para-quaternionic manifold (M,P) of dimension bigger or equal to eight, in terms of the integrability of two or three sections of the defining rank three vector bundle P. We relate it with the integrability of the canonical almost complex structure of the twistor space and to the integrability of the canonical almost para-complex structure of the reflector space of (M,P). We show that (M, P) has plenty of locally defined, compatible, complex and para-complex structures, provided that P is para-quaternionic.

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