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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.00689 |
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| _version_ | 1866911085948305408 |
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| author | Blaga, Adara M. Nannicini, Antonella |
| author_facet | Blaga, Adara M. Nannicini, Antonella |
| contents | We show that statistical and semi-Weyl structures with torsion are invariant under conformal-projective transformations. We prove that a non-degenerate submanifold of a semi-Weyl (respectively, statistical) manifold with torsion is also a semi-Weyl (respectively, statistical) manifold with torsion, and that the induced structures of two conformal-projective equivalent semi-Weyl (respectively, statistical) structures with torsion on a manifold to a non-degenerate submanifold, are conformal-projective equivalent, too. Also, we prove that the umbilical points of a non-degenerate hypersurface in a semi-Weyl manifold with torsion are preserved by conformal-projective changes. Then we consider lightlike hypersurfaces of semi-Weyl manifolds with torsion and we describe similarities and differences with respect to the non-degenerate hypersurfaces. Finally, we show that a semi-Weyl manifold with torsion can be realized by a non-degenerate affine distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00689 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion Blaga, Adara M. Nannicini, Antonella Differential Geometry We show that statistical and semi-Weyl structures with torsion are invariant under conformal-projective transformations. We prove that a non-degenerate submanifold of a semi-Weyl (respectively, statistical) manifold with torsion is also a semi-Weyl (respectively, statistical) manifold with torsion, and that the induced structures of two conformal-projective equivalent semi-Weyl (respectively, statistical) structures with torsion on a manifold to a non-degenerate submanifold, are conformal-projective equivalent, too. Also, we prove that the umbilical points of a non-degenerate hypersurface in a semi-Weyl manifold with torsion are preserved by conformal-projective changes. Then we consider lightlike hypersurfaces of semi-Weyl manifolds with torsion and we describe similarities and differences with respect to the non-degenerate hypersurfaces. Finally, we show that a semi-Weyl manifold with torsion can be realized by a non-degenerate affine distribution. |
| title | Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2209.00689 |