The injectivity radius of Lie manifolds
Paolo Antonini, Guido De Philippis, Nicola Gigli
TL;DR
This paper proves that for any compatible Riemannian metric on a Lie manifold, the injectivity radius is always positive, ensuring certain geometric regularity.
Contribution
It provides a direct geometric proof that the injectivity radius of Lie manifolds with compatible metrics is positive, a result previously less explicitly established.
Findings
Injectivity radius is positive for all compatible metrics on Lie manifolds
Provides a direct geometric proof of this positivity
Ensures geometric regularity of Lie manifolds
Abstract
We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds