Notes concerning Codazzi pairs on almost anti-Hermitian manifolds

Let backward difference be a linear connection on a 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 degrees 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 the relations of these conjugate connections, we prove a result stating that conjugations along with an identity operation together act as a Klein group, which is analogue to the known result for the Hermitian case in [2]. Secondly, we give some results exhibiting occurrences of Codazzi pairs which generalize parallelism relative to backward difference . Under the assumption that ( backward difference , J) being a Codazzi pair, we derive a necessary and sufficient condition the almost anti-Hermitian manifold (M, J, g, G) is an anti-Kahler relative to a torsion-free linear connection backward difference . Finally, we investigate statistical structures on M under backward difference ( backward difference is a J-parallel torsion-free connection).

Journal

APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B

Year

2023

Volume

38

Issue

2

Pages

223-234

ISSN

1005-1031

eISSN

1993-0445

DOI

10.1007/s11766-023-4075-3

WoS UID

WOS:001018603600006