Positive Ricci curvature through Cheeger deformations
@inproceedings{Cavenaghi2018PositiveRC, title={Positive Ricci curvature through Cheeger deformations}, author={Leonardo Francisco Cavenaghi and Renato J.M. e Silva and Llohann D. Sperancca}, year={2018} }
. This paper is devoted to a deep analysis of the process known as Cheeger deformation, applied to manifolds with isometric group actions. Here, we provide new curvature estimates near singular orbits and present several applications. As the main result, we answer a question raised by a seminal result of Searle–Wilhelm about lifting positive Ricci curvature from the quotient of an isometric action. To answer this question, we develop techniques that can be used to provide a substantially…
2 Citations
The Petersen--Wilhelm conjecture on principal bundles
- Mathematics
- 2022
. In this paper we study Cheeger deformations on S 3 ,SO (3) principal bundles to obtain conditions to the existence of submersion metrics of positive sectional curvature on these. We conclude, in…
The concept of Cheeger deformations on fiber bundles with compact structure group
- MathematicsSão Paulo Journal of Mathematical Sciences
- 2022
The purpose of this paper is two-fold: we systematically introduce the notion of Cheeger deformations on fiber bundles with compact structure groups, and recover in a very simple and unified fashion…
References
SHOWING 1-10 OF 43 REFERENCES
AN EXOTIC T1S 4 WITH POSITIVE CURVATURE
- Mathematics
- 2011
We construct a metric with positive sectional curvature on a 7-manifold which supports an isometry group with orbits of codimension 1. It is a connection metric on the total space of an orbifold…
Scalar curvature
- MathematicsGraduate Studies in Mathematics
- 2019
We shall deal with some problems concerning the scalar curvature of compact riemannian manifolds. In particular we shall deal with the problem of Yamabe: Does there exist a conformal metric for which…
Curvature and symmetry of Milnor spheres
- Mathematics, Physics
- 2000
Since Milnor’s discovery of exotic spheres [Mi], one of the most intriguing problems in Riemannian geometry has been whether there are exotic spheres with positive curvature. It is well known that…
How to lift positive Ricci curvature
- Mathematics
- 2015
Remark Various definitions of lower Ricci curvature bounds on metric spaces are proposed in Kuwae and Shioya [23], Lott and Villani [25], Ohta [28], Sturm [40; 41] and Zhang and Zhu [50]. Our proof…
Krummüngserhöhende deformationen mittels gruppenaktionen
- PhD thesis, Westfälischen Wilhelms-Universität Münster
- 1987
Highly connected 7-manifolds and non-negative sectional curvature
- MathematicsAnnals of Mathematics
- 2020
Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper…
Positive Ricci curvature on fibre bundles
- Mathematics
- 1979
In this paper we construct complete metrics of positive Ricci curvature on a large class of fibre bundles. Some of the results for compact fibres have been obtained independently by Poor [12]. The…
Invariant metrics of positive Ricci curvature on principal bundles
- Mathematics
- 1998
Abstract. Let
$Y$ be a compact connected Riemannian manifold with a metric of positive Ricci curvature. Let
$\pi:P\rightarrow Y$ be a principal bundle over
$Y$ with compact connected structure…