@article{Rovenski2026, 
author = {Vladimir Rovenski and Milan Zlatanović},
title = {Einstein connection of nonsymmetric pseudo-Riemannian manifold with the        f    2  -torsion condition},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {18481-18501},
keywords = {nonsymmetric pseudo-Riemannian manifold, weak almost Hermitian manifold, Einstein connection, almost contact metric structure, f2-torsion condition},
url = {https://www.sciopen.com/article/10.3934/math.2026751},
doi = {10.3934/math.2026751},
abstract = {Einstein considered a linear connection    ∇ with torsion    T on a differentiable manifold equipped with a nonsymmetric (0, 2)-tensor    G  =  g  +  F, where    g is a pseudo-Riemannian metric associated with gravity, and    F  ≠  0 is a skew-symmetric tensor associated with electromagnetism, such that    (      ∇    X      G  )  (  Y  ,  Z  )  =  −  G  (  T  (  X  ,  Y  )  ,  Z  ). In this paper, we explicitly present the Einstein connection of a nonsymmetric pseudo-Riemannian manifold with non-degenerate    F, satisfying the        f    2  -torsion condition    T  (      f    2    X  ,  Y  )  =  T  (  X  ,      f    2    Y  )  =      f    2    T  (  X  ,  Y  ), where    g  (  X  ,  f  Y  )  =  F  (  X  ,  Y  ), and show that in the almost Hermitian case, it reduces to the Prvanović's (1995) solution. We also explicitly present the Einstein connection of almost contact metric manifolds satisfying the        f    2  -torsion condition, discuss special Einstein connections, and give example in terms of the weighted product of almost Hermitian manifolds.}
}