[图书][B] Riemannian manifolds and homogeneous geodesics
V Berestovskii, Y Nikonorov - 2020 - Springer
The main purpose of this book is to give an exposition of recent results (obtained with the
essential participation of the authors) on geodesic orbit Riemannian manifolds and their …
essential participation of the authors) on geodesic orbit Riemannian manifolds and their …
Hausdorff convergence of Riemannian manifolds and its applications
K Fukaya - Recent topics in differential and analytic geometry, 1990 - Elsevier
Publisher Summary This chapter discusses the theory of Hausdorff convergence.
Classically, the Hausdorff distance between two closed subsets in a fixed metric space has …
Classically, the Hausdorff distance between two closed subsets in a fixed metric space has …
Critical point theory for distance functions
K Grove - Proceedings of Symposia in Pure Mathematics, 1993 - books.google.com
One of the fundamental themes in riemannian geometry is to relate properties of a
riemannian manifold as a metric space to differential topological properties of it as a smooth …
riemannian manifold as a metric space to differential topological properties of it as a smooth …
Geometry of, and via, symmetries
K Grove - University Lecture Series-American Mathematical …, 2002 - books.google.com
It is well known that Lie groups and homogeneous spaces provide a rich source of
interesting examples for a variety of geometric aspects. Likewise it is often the case that …
interesting examples for a variety of geometric aspects. Likewise it is often the case that …
The topoligical sphere theorem for complete submanifolds
K Shiohama, H Xu - Compositio Mathematica, 1997 - cambridge.org
A topological sphere theorem is obtained from the point of view of submanifold geometry. An
important scalar is defined by the mean curvature and the squared norm of the second …
important scalar is defined by the mean curvature and the squared norm of the second …
Collapsing three-manifolds under a lower curvature bound
T Shioya, T Yamaguchi - Journal of Differential Geometry, 2000 - projecteuclid.org
COLLAPSING THREE-MANIFOLDS UNDER A LOWER CURVATURE BOUND Page 1 j.
differential geometry 56 (2000) 1-66 COLLAPSING THREE-MANIFOLDS UNDER A LOWER …
differential geometry 56 (2000) 1-66 COLLAPSING THREE-MANIFOLDS UNDER A LOWER …
[PDF][PDF] Nonnegatively and positively curved manifolds
B Wilking - arXiv preprint arXiv:0707.3091, 2007 - arxiv.org
arXiv:0707.3091v1 [math.DG] 20 Jul 2007 Page 1 arXiv:0707.3091v1 [math.DG] 20 Jul 2007
NONNEGATIVELY AND POSITIVELY CURVED MANIFOLDS BURKHARD WILKING The aim of …
NONNEGATIVELY AND POSITIVELY CURVED MANIFOLDS BURKHARD WILKING The aim of …
Manifolds near the boundary of existence
K Grove, P Petersen - Journal of Differential Geometry, 1991 - projecteuclid.org
Our primary purpose is to study relationships between bounds on sectional curvature KM,
diameter dM, and volume VM, together with their effects on the topology of closed …
diameter dM, and volume VM, together with their effects on the topology of closed …
[PDF][PDF] A radius sphere theorem
K Grove, P Petersen - Inventiones mathematicae, 1993 - researchgate.net
The purpose of this paper is to present an optimal sphere theorem for metric spaces
analogous to the celebrated Rauch-Berger-Klingenberg Sphere Theorem and the Diameter …
analogous to the celebrated Rauch-Berger-Klingenberg Sphere Theorem and the Diameter …
Index parity of closed geodesics and rigidity of Hopf fibrations
B Wilking - Inventiones mathematicae, 2001 - Springer
The diameter rigidity theorem of Gromoll and Grove [1987] states that a Riemannian
manifold with sectional curvature≥ 1 and diameter≥ π/2 is either homeomorphic to a …
manifold with sectional curvature≥ 1 and diameter≥ π/2 is either homeomorphic to a …