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arXiv · 2209.00689

Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion

Adara M. Blaga·Antonella Nannicini
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Abstract

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.

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Adara M. Blaga, Antonella Nannicini. 2022-09-01. Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion. https://doi.org/10.55730/1300-0098.3518

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