Distance Functions, Curvature and Topology
Carlo Mantegazza, Francesca Oronzio
TL;DR
This paper explores how distance functions on Riemannian manifolds relate to their curvature and topology, providing new proofs of classical theorems in differential geometry.
Contribution
It offers alternative proofs connecting curvature and topology through properties of distance functions on Riemannian manifolds.
Findings
Properties of distance functions are linked to manifold geometry
Alternative proofs of classical curvature-topology theorems
Insights into the relationship between curvature, topology, and distance functions
Abstract
We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis