Almost complex connections on almost complex manifolds with Norden metric. (English) Zbl 1183.53015

Teofilova, Marta

Sekigawa, Kouei (ed.) et al., Trends in differential geometry, complex analysis and mathematical physics. Proceedings of 9th international workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, August 25–29, 2008. Hackensack, NJ: World Scientific (ISBN 978-981-4277-71-6/hbk). 231-240 (2009).

Summary: A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A two-parametric family of complex connections is studied on a conformal Kähler manifold with Norden metric. The curvature tensors of these connections are proved to coincide.
For the entire collection see [Zbl 1177.53007].

MSC:

53B05	Linear and affine connections
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

almost complex manifold; Norden metric; complex connection