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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.09532 |
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| _version_ | 1866917176857853952 |
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| author | Rovenski, Vladimir |
| author_facet | Rovenski, Vladimir |
| contents | A. Einstein considered a manifold with a non-symmetric (0,2)-tensor $G=g+F$, where $g$ is a Riemannian metric and $F\ne0$, and a connection $\nabla$ with torsion $T$ such that $(\nabla_X G)(Y,Z)=-G(T(X,Y),Z)$. Guided by the almost Lie algebroid construction on a vector bundle, we define the basic concepts of Bochner's technique for Einstein's non-symmetric geometry, give a clear example of the Einstein's connection $\nabla$, prove Weitzenböck type decomposition formula and obtain vanishing results about the null space of the Bochner and Hodge type Laplacians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bochner's technique in Einstein's non-symmetric geometry Rovenski, Vladimir Differential Geometry A. Einstein considered a manifold with a non-symmetric (0,2)-tensor $G=g+F$, where $g$ is a Riemannian metric and $F\ne0$, and a connection $\nabla$ with torsion $T$ such that $(\nabla_X G)(Y,Z)=-G(T(X,Y),Z)$. Guided by the almost Lie algebroid construction on a vector bundle, we define the basic concepts of Bochner's technique for Einstein's non-symmetric geometry, give a clear example of the Einstein's connection $\nabla$, prove Weitzenböck type decomposition formula and obtain vanishing results about the null space of the Bochner and Hodge type Laplacians. |
| title | Bochner's technique in Einstein's non-symmetric geometry |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.09532 |