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About the geometry of almost para-quaternionic manifolds
- Source :
- Differential Geometry and its Applications. (5):575-588
- Publisher :
- Elsevier B.V.
-
Abstract
- 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.<br />26 pages
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Integrable system
Twistor and reflector spaces
Structure (category theory)
Vector bundle
53C15, 53C25
Rank (differential topology)
Space (mathematics)
Almost para-quaternionic manifolds
Manifold
Differential Geometry (math.DG)
Computational Theory and Mathematics
Dimension (vector space)
FOS: Mathematics
Twistor space
Geometry and Topology
Analysis
Mathematics
Compatible complex and para-complex structures
Subjects
Details
- Language :
- English
- ISSN :
- 09262245
- Issue :
- 5
- Database :
- OpenAIRE
- Journal :
- Differential Geometry and its Applications
- Accession number :
- edsair.doi.dedup.....fd271f849aa7bc9b6de378e788764662
- Full Text :
- https://doi.org/10.1016/j.difgeo.2009.01.014