Structure-preserving connections on almost complex Norden golden manifolds

• Published in: Journal of geometry 2019-12, Vol.110 (3), p.1-20, Article 55
• Main Authors: Zhong, Shiping, Zhao, Zehui, Mu, Gui
• Format: Article
• Language: English
• Subjects: Geometry; Manifolds; Mathematical analysis; Mathematics; Mathematics and Statistics; Tensors
• ISSN: 0047-2468; 1420-8997
• DOI: 10.1007/s00022-019-0511-1

An almost complex Norden golden structure ( G c , g ) on a manifold is given by a tensor field G c of type (1, 1) satisfying the complex golden section relation G c 2 = G c - 3 2 Id , and a pure pseudo-Riemannian metric g , i.e., a metric satisfying g ( G c X , Y ) = g ( X , G c Y ) . In this paper some structure-preserving connections including twin Norden golden metric-preserving connections, G c -metric-preserving connections, G c -preserving connections are studied. Twin Norden golden metric-preserving connections could be completed specifying those conditions. Also G c -metric-preserving connections are analyzed and we show that every Kähler–Norden–Codazzi golden manifold is a Kähler–Norden golden manifold, a consequence many of results in Bilen et al. (Int J Geom Methods Mod Phys 15(5):1850080, 2018) could be simplified. Finally, G c -preserving connections are investigated and we show that G c -preserving connections are determined by the skew-symmetry and pureness of an associated 3-tensor.