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A CHARACTERIZATION OF THE REAL PROJECTIVE PLANE

JOËL ROUYER

16 Rue Philippe, 68220 Hegenheim, France

https://doi.org/10.1142/S0129167X10006653Cited by:0 (Source: Crossref)

Abstract

It is proved in this article, that in the framework of Riemannian geometry, the existence of large sets of antipodes (i.e. farthest points) for diametral points of a smooth surface has very strong consequences on the topology and the metric of this surface. Roughly speaking, if the sets of antipodes of diametral points are closed curves, then the surface is nothing but the real projective plane.

Keywords:

AMSC: 53C20, 53C45

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