Conformal product structures on compact manifolds with constant sectional curvature

TL;DR

This paper proves that compact non-flat manifolds with constant sectional curvature cannot have conformal product structures, and extends the methods to certain symmetric spaces.

Contribution

It establishes a non-existence result for conformal product structures on specific curved manifolds and broadens the approach to other symmetric spaces.

Findings

No conformal product structures on compact non-flat constant curvature manifolds.

Methods extend to irreducible, compact locally symmetric spaces of non-positive curvature.

Provides a framework for analyzing conformal structures on curved manifolds.

Abstract

We prove that compact non-flat manifolds with constant sectional curvature admit no conformal product structure. Furthermore, we demonstrate that the methods extend naturally to irreducible, compact locally symmetric spaces of non-positive curvature.