Centrally Harmonic spaces
Peter Gilkey, JeongHyeong Park
TL;DR
This paper constructs examples of centrally harmonic spaces, explores their properties, and demonstrates that such spaces can have Euclidean-like density functions without being conformally flat.
Contribution
It generalizes previous work to produce new examples of centrally harmonic spaces and analyzes their geometric properties.
Findings
Examples of centrally harmonic spaces are constructed.
Most such spaces are not centrally harmonic at all points.
Some manifolds have Euclidean density functions but are not conformally flat.
Abstract
We construct examples of centrally harmonic spaces by generalizing work of Copson and Ruse. We show that these examples are generically not centrally harmonic at other points. We use this construction to exhibit manifolds which are not conformally flat but such that their density function agrees with Euclidean space.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology