Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two

TL;DR

This paper proves a significant partial case of the pseudo-Riemannian projective Lichnerowicz conjecture, showing that complete manifolds with an essential group of projective transformations are essentially round spheres.

Contribution

It establishes a partial proof of the conjecture for pseudo-Riemannian metrics with certain properties, advancing understanding of geometric transformation groups.

Findings

Complete manifolds with essential projective transformation groups are round spheres.

Partial proof of the pseudo-Riemannian projective Lichnerowicz conjecture.

Advances in understanding the structure of manifolds with symmetries.

Abstract

We prove an important partial case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the round sphere (up to a finite cover).