Notes concerning Codazzi pairs on almost anti-Hermitian manifolds  

作　　者：Aydin Gezer Hasan Cakicioglu 

机构地区：[1]Department of Mathematics,Ataturk University,25240,Erzurum-Turkey

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2023年第2期223-234,共12页高校应用数学学报（英文版）（B辑）

摘　　要：Let∇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◦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∇.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-K¨ahler relative to a torsion-free linear connection∇.Finally,we investigate statistical structures on M under∇(∇is a J−parallel torsion-free connection).

关 键 词：anti-Kahler structure Codazzi pair conjugate connection twin metric statistical structure 

分 类 号：O186.1[理学—数学]