Einstein connection of nonsymmetric pseudo-Riemannian manifold
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911540146339840 |
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| author | Rovenski, Vladimir Zlatanović, Milan |
| author_facet | Rovenski, Vladimir Zlatanović, Milan |
| contents | A.Einstein considered a linear connection $\nabla$ with torsion $T$ on a smooth manifold equipped with a nonsymmetric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric tensor associated with electromagnetism, such that $(\nabla_X\,G)(Y,Z)=-G(T(X,Y),Z)$. 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 $T(f^2X,Y)=T(X,f^2Y)=f^2 T(X,Y)$, where $g(X,fY)=F(X,Y)$, and show that in the almost Hermitian case, it reduces to the M.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 weighted product of almost Hermitian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Einstein connection of nonsymmetric pseudo-Riemannian manifold Rovenski, Vladimir Zlatanović, Milan Differential Geometry Mathematical Physics 53B05, 53C15, 53C21 A.Einstein considered a linear connection $\nabla$ with torsion $T$ on a smooth manifold equipped with a nonsymmetric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric tensor associated with electromagnetism, such that $(\nabla_X\,G)(Y,Z)=-G(T(X,Y),Z)$. 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 $T(f^2X,Y)=T(X,f^2Y)=f^2 T(X,Y)$, where $g(X,fY)=F(X,Y)$, and show that in the almost Hermitian case, it reduces to the M.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 weighted product of almost Hermitian manifolds. |
| title | Einstein connection of nonsymmetric pseudo-Riemannian manifold |
| topic | Differential Geometry Mathematical Physics 53B05, 53C15, 53C21 |
| url | https://arxiv.org/abs/2602.15956 |