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

TL;DR

This paper investigates how conformal-projective transformations affect statistical and semi-Weyl manifolds with torsion, demonstrating invariance properties, submanifold behavior, and geometric features like umbilical points and lightlike hypersurfaces.

Contribution

It establishes invariance of structures under conformal-projective transformations and explores submanifold and hypersurface properties in semi-Weyl manifolds with torsion.

Findings

Statistical and semi-Weyl structures with torsion are invariant under conformal-projective transformations.

Non-degenerate submanifolds inherit semi-Weyl or statistical structures with torsion.

Umbilical points are preserved under conformal-projective changes.

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.