2019/11/12 by Aydın Gezer, Gezer, Aydin, Hasan Çakıcıoğlu +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1911.06140
Let ∇ be a linear connection on an 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J, a pseudo-Riemannian metric g and the twin metric G=g∘ J. In this paper, we first introduce three types of conjugate connections of linear connections relative to g, G and J. We obtain a simple relation among curvature tensors of these conjugate connections. To clarify relations of these conjugate connections, we prove a result stating that conjugations along with an identity operation together act as a Klein group. Secondly, we give some results exhibiting occurrences of Codazzi pairs which generalize parallelism relative to ∇ . Under the assumption that (∇ ,J) being a Codazzi pair, we derive a necessary and sufficient condition the almost anti-Hermitian manifold (M,J,g,G) is an anti-Kähler relative to a torsion-free linear connection ∇ . Finally, we investigate statistical structures on M under ∇ (∇ is a J-invariant torsion-free connection).