Weak metric structures on generalized Riemannian manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911334139953152 |
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| author | Rovenski, Vladimir Zlatanović, Milan |
| author_facet | Rovenski, Vladimir Zlatanović, Milan |
| contents | In the paper, we first study more general models, where $F$ has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric $f$-contact structures. We consider generalized metric connections (i.e., linear connections preserving $G$) with totally skew-symmetric torsion (0,3)-tensor. For rank$(F)=\dim M$ and non-conformal tensor $A^2$, where $A$ is a skew-symmetric (1,1)-tensor adjoint to $F$, we apply weak almost Hermitian structures to fundamental results (by the second author and S. Ivanov) on generalized Riemannian manifolds and prove that the manifold is a weighted product of several nearly Kähler manifolds corresponding to eigen-distributions of $A^2$. For rank$(F)<\dim M$ we apply weak $f$-structures and obtain splitting results for generalized Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak metric structures on generalized Riemannian manifolds Rovenski, Vladimir Zlatanović, Milan Differential Geometry 53C15, 53C25, 53B05 In the paper, we first study more general models, where $F$ has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric $f$-contact structures. We consider generalized metric connections (i.e., linear connections preserving $G$) with totally skew-symmetric torsion (0,3)-tensor. For rank$(F)=\dim M$ and non-conformal tensor $A^2$, where $A$ is a skew-symmetric (1,1)-tensor adjoint to $F$, we apply weak almost Hermitian structures to fundamental results (by the second author and S. Ivanov) on generalized Riemannian manifolds and prove that the manifold is a weighted product of several nearly Kähler manifolds corresponding to eigen-distributions of $A^2$. For rank$(F)<\dim M$ we apply weak $f$-structures and obtain splitting results for generalized Riemannian manifolds. |
| title | Weak metric structures on generalized Riemannian manifolds |
| topic | Differential Geometry 53C15, 53C25, 53B05 |
| url | https://arxiv.org/abs/2506.23019 |