A Pinching constant for harmonic manifolds
K. Ramachandran, Akhil Ranjan (Dept of Mathematics, Indian, Institute of Technology, Mumbai, India)
TL;DR
This paper establishes a bounded pinching constant for the sectional curvature of harmonic manifolds, using Szabo's embedding theorem and screw lines in Hilbert spaces to prove the result.
Contribution
It introduces a specific pinching constant for harmonic manifolds' sectional curvature, advancing understanding of their geometric properties.
Findings
Sectional curvature of harmonic manifolds is bounded on both sides.
A pinching constant for all harmonic manifolds is provided.
The proof utilizes Szabo's embedding theorem and screw lines in Hilbert spaces.
Abstract
In this note we shall show that the sectional curvature of a harmonic manifold is bounded on both sides. In fact we shall give a pinching constant for all harmonic manifolds. We shall use the imbedding theorem for harmonic manifolds proved by Z.I.Szabo and the description of screw lines in hilbert spaces to prove the result.
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 · Geometry and complex manifolds · Point processes and geometric inequalities