Besse Projective Spaces with Many Diameters

Besse Projective Spaces with Many Diameters

It is known that Blaschke manifolds (where injectivity radius equals diameter) are Besse manifolds (where all geodesics are closed). We show that Besse manifolds with sufficiently many diameter realizing directions are Blaschke. We also provide bounds in terms of diameter on the length of the shorte...

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Veröffentlicht in:The Journal of Geometric Analysis 2023-09, Vol.33 (9), Article 277
Hauptverfasser: Adelstein, Ian, Pallete, Franco Vargas
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Diameters
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geodesy
Geometry
Global Analysis and Analysis on Manifolds
Manifolds
Mathematics
Mathematics and Statistics
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Zusammenfassung:It is known that Blaschke manifolds (where injectivity radius equals diameter) are Besse manifolds (where all geodesics are closed). We show that Besse manifolds with sufficiently many diameter realizing directions are Blaschke. We also provide bounds in terms of diameter on the length of the shortest closed geodesic for pinched curvature metrics on simply connected manifolds.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01337-3