On Almost Norden Statistical Manifolds

Abstract

We consider a statistical connection ∇ on an almost complex manifold with (pseudo-) Riemannian metric, in particular the Norden metric. We investigate almost Norden (statistical) manifolds under the condition that the almost complex structure J is ∇-recurrent. We provide one example of a complex statistical connection.

The Translation Surfaces on Statistical Manifolds with Normal Distribution

“…Later on, this theory found applications in various areas of geometry as almost-contact geometry, [1], [22], [35], [47] , Hermitian-Kaehler geometry, [2], [21], [42], [43]. [55], [64], almost Norden manifolds [51], almost paracontact geometry [13], submersions [11], [36], [60] [61] [62] and Hessian geometry [29].…”

Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

“…The authors proved that the pair (∇, L) is torsion-coupled if and only if ∇ is (para-)holomorphic and the almost (para-)complex structure L is integrable. Statistical structures on almost anti-Hermitian (or Norden) manifolds were studied in [26,27] by A. Salimov and S. Turanli, who introduced the notion of anti-Kähler-Codazzi manifolds, then by L. Samereh, E. Peyghan, and I. Mihai in [28], and very recently by A. Gezer and H. Cakicioglu, who provided in [10] an alternative classification of anti-Kähler manifolds with respect to a torsion-free linear connection. Codazzi pairs on almost para-Norden manifolds were treated by S. Turanli and S. Uçan in [29].…”

Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds

“…Crasmareanu and Hretcanu also defined the almost complex golden manifold in the same paper [3]. Later, these manifolds were studied by many authors [5][6][7][8][9][10][11]. However, as far as we know, there has been no study in the literature about the sectional curvature of such manifolds.…”