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- Title
Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion.
- Authors
BLAGA, Adara M.; NANNICINI, Antonella
- Abstract
We show that statistical and semi-Weyl structures with torsion are invariant under conformal-projective transformations. We prove that a nondegenerate 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 nondegenerate submanifold, are conformal-projective equivalent, too. Also, we prove that the umbilical points of a nondegenerate 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 nondegenerate hypersurfaces. Finally, we show that a semi-Weyl manifold with torsion can be realized by a nondegenerate affine distribution.
- Subjects
HYPERSURFACES; SUBMANIFOLDS; TORSION
- Publication
Turkish Journal of Mathematics, 2024, Vol 48, Issue 3, p448
- ISSN
1300-0098
- Publication type
Article
- DOI
10.55730/1300-0098.3518