Finsler conformal Lichnerowicz-Obata conjecture
Vladimir S. Matveev, Hans-Bert Rademacher, Marc Troyanov, and, Abdelghani Zeghib
TL;DR
This paper proves a Finsler geometry version of the conformal Lichnerowicz-Obata conjecture, demonstrating that certain conformal vector fields on non-Riemannian Finsler manifolds are homothetic for Minkowski metrics.
Contribution
It establishes the Finsler analog of the conjecture, identifying the nature of conformal vector fields on non-Riemannian Finsler manifolds.
Findings
Conformal vector fields are homothetic in Minkowski spaces.
Complete and essential conformal vector fields imply a Minkowski metric.
Extension of classical Riemannian results to Finsler geometry.
Abstract
We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.
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Taxonomy
TopicsAdvanced Differential Geometry Research