Soft restrictions on positively curved Riemannian submersions

TL;DR

This paper establishes bounds on the fiber dimension of positively curved Riemannian submersions based on the base manifold's dimension and geometric properties like conjugate radius or shortest closed geodesic length.

Contribution

It introduces new bounds relating fiber dimension to base manifold properties in positively curved Riemannian submersions.

Findings

Bound on fiber dimension in terms of base dimension and conjugate radius.

Bound on fiber dimension using shortest closed geodesic length.

Results applicable to positively curved Riemannian submersions.

Abstract

We bound the dimension of the fiber of a Riemannian submersion from a positively curved manifold in terms of the dimension of the base of the submersion and either its conjugate radius or the length of its shortest closed geodesic.