Zobrazeno 1 - 10
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pro vyhledávání: '"Grove, Karsten"'
Autor:
Grove, Karsten, Petersen, Peter
Publikováno v:
Geom. Topol. 26 (2022) 1635-1668
Abstract. In this paper we prove several rigidity theorems related to and including Lytchak's problem. The focus is on Alexandrov spaces with \curv\geq1, nonempty boundary, and maximal radius \frac{\pi}{2}. We exhibit many such spaces that indicate t
Externí odkaz:
http://arxiv.org/abs/1805.10221
We prove that the boundary of an orbit space or more generally a leaf space of a singular Riemannian foliation is an Alexandrov space in its intrinsic metric, and that its lower curvature bound is that of the leaf space. A rigidity theorem for positi
Externí odkaz:
http://arxiv.org/abs/1804.01656
Publikováno v:
Communications in Analysis and Geometry, 24(2016), 487-520
An axiomatic characterization of buildings of type $\CC_3$ due to Tits is used to prove that any cohomogeneity two polar action of type $\CC_3$ on a positively curved simply connected manifold is equivariantly diffeomorphic to a polar action on a ran
Externí odkaz:
http://arxiv.org/abs/1607.04134
Autor:
Chen, Xiaoyang, Grove, Karsten
We derive general structure and rigidity theorems for submetries $f: M \to X$, where $M$ is a Riemannian manifold with sectional curvature $\sec M \ge 1$. When applied to a non-trivial Riemannian submersion, it follows that $diam X \leq \pi/2 $. In c
Externí odkaz:
http://arxiv.org/abs/1404.3777
Autor:
Fang, Fuquan, Grove, Karsten
Publikováno v:
Journal of Differential Geometry 102 (2016), 179-205
We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, and moreover, classify such W. In particular, we show that the building
Externí odkaz:
http://arxiv.org/abs/1403.5019
Autor:
Grove, Karsten, Wilking, Burkhard
Publikováno v:
Geom. Topol. 18 (2014) 3091-3110
We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular set of the orbit space. As an extension of this work we classify all kno
Externí odkaz:
http://arxiv.org/abs/1304.4827
Autor:
Grove, Karsten, Searle, Catherine
Publikováno v:
Journal of Pure and Applied Algebra, 91 (1994), pp. 137--142
The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.
Externí odkaz:
http://arxiv.org/abs/1208.1206
Autor:
Grove, Karsten, Ziller, Wolfgang
A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. Such group actions have been studied extensively on symmetric spaces. We show how to construct a manifold admitting a polar g
Externí odkaz:
http://arxiv.org/abs/1208.0976
Autor:
Grove, Karsten, Searle, Catherine
Publikováno v:
Annals of Global Analysis and Geometry, 18, pp. 437--446 (2000)
The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.
Externí odkaz:
http://arxiv.org/abs/1207.4423
There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact
Externí odkaz:
http://arxiv.org/abs/1205.6222