2023/05/31 by Aydın Gezer, Gezer, Aydin, Buşra Aktaş +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2307.15065
openalex publication_date 2023/05/31 · openalex created_date 2023/08/01 · openalex updated_date 2026/07/28
Let (\acuteN,g,∇ ) be a 2n-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric g (or h) and a linear connection ∇ with torsion. This paper aims to study an almost Hermitian structure (g,L) and an almost anti-Hermitian structure (h,L) on a quasi-statistical manifold that admit an almost complex structure L. Firstly, under certain conditions, we present the integrability of the almost complex structure L. We show that when d^∇ L =0 and the condition of torsion-compatibility are satisfied, (\acuteN,g,∇ , L) turns into a Kähler manifold. Secondly, we give necessary and sufficient conditions under which (\acuteN,h,∇ ,L) is an anti-Kä% hler manifold, where h is an anti-Hermitian metric. Moreover, we search the necessary conditions for (\acuteN,h,∇ ,L) to be a quasi-Kähler-Norden manifold.