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arXiv:math.DG/0703450v115Mar2007 Hermitian and quaternionic Hermitian structures on
 

Summary: arXiv:math.DG/0703450v115Mar2007
Hermitian and quaternionic Hermitian structures on
tangent bundles
Rui Albuquerque
rpa@dmat.uevora.pt
March 15, 2007
Abstract
We review the theory of quaternionic Kšahler and hyperkšahler structures. Then
we consider the tangent bundle of a Riemannian manifold M with a metric con-
nection D (with torsion) and with its well estabilished canonical complex structure.
With an extra almost Hermitian structure on M it is possible to find a quaternionic
Hermitian structure on TM, which is quaternionic Kšahler if, and only if, D is flat
and torsion free. We also review the symplectic nature of TM. Finally a proper
S3-bundle of complex structures is introduced, expanding to TM the well known
twistor bundle of M.
Key Words: torsion, quaternionic, Hermitian, Kšahler, symplectic.
MSC 2000: 53C15, 53C26, 53C55.
The author acknowledges the support of Fundažc~ao Ci^encia e Tecnologia, through the
research center CIMA - Universidade de ŽEvora and through the project POCI/MAT/-
60671/2004.

  

Source: Albuquerque, Rui - Departamento de Matemática, Universidade de Évora

 

Collections: Mathematics