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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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A possible characterization of sphere or projective space

The article by X. Liu and Sh. Deng "The antipodal sets of compact symmetric spaces" gives many examples, e.g. $\mathrm{SU}(2n)$, $\mathrm{Spin}(5)$, $\mathrm{Spin}(7)$,.... All those spaces have uniqu …
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