Hermitian and quaternionic Hermitian structures on tangent bundles

被引：0
作者：
Rui Albuquerque
机构：
[1] Centro de Investigação em Matemática e Aplicações (CIMA),Departamento de Matemática
[2] Universidade de Évora,undefined
来源：
Geometriae Dedicata | 2008年 / 133卷
关键词：
Torsion; Quaternionic; Hermitian; Kähler; Symplectic; 53C15; 53C26; 53C55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We review the theory of quaternionic Kähler and hyperkähler structures. Then we consider the tangent bundle of a Riemannian manifold M endowed with a metric connection D, with torsion, and with its well estabilished canonical complex structure. With an almost Hermitian structure on M it is possible to find a quaternionic Hermitian structure on TM, which is quaternionic Kähler if, and only if, D is flat and torsion free. We also review the symplectic nature of TM, in the wider context of geometry with torsion. Finally we discover an S3-bundle of complex structures, which expands to TM the well known S2-twistor bundle of a quaternionic Hermitian manifold M.
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页码：95 / 110
页数：15
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