Positively curved manifolds with large spherical rank
نویسندگان
چکیده
منابع مشابه
Positively Curved Manifolds with Large Spherical Rank
Rigidity results are obtained for Riemannian d-manifolds with sec > 1 and spherical rank at least d − 2 > 0. Conjecturally, all such manifolds are locally isometric to a round sphere or complex projective space with the (symmetric) Fubini– Study metric. This conjecture is verified in all odd dimensions, for metrics on dspheres when d 6= 6, for Riemannian manifolds satisfying the Rakić duality p...
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We present two theorems in the “discrete differential geometry” of positively curved spaces. The first is a combinatorial analog of the Bonnet-Myers theorem: • A combinatorial 3-manifold whose edges have degree at most five has edgediameter at most five. When all edges have unit length, this degree bound is equivalent to an angle-deficit along each edge. It is for this reason we call such space...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2016
ISSN: 0010-2571
DOI: 10.4171/cmh/384