Zobrazeno 1 - 10
of 67
pro vyhledávání: '"Wilking, Burkhard"'
Autor:
Lytchak, Alexander, Wilking, Burkhard
We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of the base is
Externí odkaz:
http://arxiv.org/abs/2411.15324
We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.
Comment: Added Lemma
Comment: Added Lemma
Externí odkaz:
http://arxiv.org/abs/2310.12307
We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the former objects, we obtain a classification of the latter. In addition,
Externí odkaz:
http://arxiv.org/abs/2212.08152
Publikováno v:
Advances In Mathematics 441 (2024)
We study isometric actions of compact Lie groups on complete orientable positively curved $n$-manifolds whose orbit spaces have non-empty boundary in the sense of Alexandrov geometry. In particular, we classify quotients of the unit sphere by actions
Externí odkaz:
http://arxiv.org/abs/2112.00513
Publikováno v:
In Advances in Mathematics April 2024 441
A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold with positive sectional curvature has positive Euler characteristic. We prove this conjecture under the additional assumption that the isometry group has rank at l
Externí odkaz:
http://arxiv.org/abs/2106.14723
We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics wh
Externí odkaz:
http://arxiv.org/abs/1707.03002
Autor:
Radeschi, Marco, Wilking, Burkhard
A conjecture of Berger states that, for any simply connected Riemannian manifold all of whose geodesics are closed, all prime geodesics have the same length. We firstly show that the energy function on the free loop space of such a manifold is a perf
Externí odkaz:
http://arxiv.org/abs/1511.07852
Autor:
Wilking, Burkhard, Ziller, Wolfgang
As was recently observed by M. Xu and J. Wolf, there is a gap in Berard Bergery's classification of odd dimensional positively curved homogeneous spaces. Since this classification has been used in other papers as well, we give a modern, complete and
Externí odkaz:
http://arxiv.org/abs/1503.06256
Autor:
Lytchak, Alexander, Wilking, Burkhard
Publikováno v:
Geom. Topol. 20 (2016) 1257-1274
We show that a Riemannian foliation on a topological $n$-sphere has leaf dimension 1 or 3 unless n=15 and the Riemannian foliation is given by the fibers of a Riemannian submersion to an 8-dimensional sphere. This allows us to classify Riemannian fol
Externí odkaz:
http://arxiv.org/abs/1309.7884