Besse projective spaces with many diameters

Ian Adelstein; Franco Vargas Pallete

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arXiv · 2201.03676

Besse projective spaces with many diameters

Ian Adelstein·Franco Vargas Pallete

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Abstract

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.

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Ian Adelstein, Franco Vargas Pallete. 2022-01-10. Besse projective spaces with many diameters. https://arxiv.org/abs/2201.03676

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