Some Regularity of submetries

TL;DR

This paper investigates the regularity properties of submetries in Riemannian geometry, demonstrating that quotient space strata have curvature bounded on both sides, which advances understanding of geometric decomposition.

Contribution

It provides new regularity results for equidistant decompositions and quotient spaces in Riemannian manifolds, highlighting curvature bounds on strata.

Findings

Strata of quotient spaces have curvature locally bounded from both sides.

Regularity statements hold for equidistant decompositions.

Results contribute to the understanding of geometric structure in Riemannian manifolds.

Abstract

We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space has curvature locally bounded from both sides.