Core reduction for singular Riemannian foliations and applications to positive curvature

Corro, Diego; Moreno, Adam

doi:10.1007/s10455-022-09856-y

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…Singular Riemannian foliations generalize both isometric compact Lie group actions and Riemannian submersions, which induce decompositions into embedded submanifolds of lower dimension, and represent a generalized notion of symmetry on Riemannian manifolds [3,10,12,19,36]. Not all singular Riemannian foliations stem from Lie group actions (see, for example, [38]).…”

Section: Resultsmentioning

confidence: 99%

Yamabe problem in the presence of singular Riemannian Foliations

Corro

Fernandez²,

Perales³

2022

Calc. Var.

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We prove that the group of isometries preserving a metric foliation on a closed Alexandrov space X, or a singular Riemannian foliation on a manifold M is a closed subgroup of the isometry group of X in the case of a metric foliation, or of the isometry group of M for the case of a singular Riemannian foliation. We obtain a sharp upper bound for the dimension of these subgroups and show that, when equality holds, the foliations that realize this upper bound are induced by fiber bundles whose fibers are round spheres or projective spaces. Moreover, singular Riemannian foliations that realize the upper bound are induced by smooth fiber bundles whose fibers are round spheres or projective spaces.

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Section: Resultsmentioning

confidence: 99%

Yamabe problem in the presence of singular Riemannian Foliations

Corro

Fernandez²,

Perales³

2022

Calc. Var.

Self Cite

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show abstract

“…Thus, in order to classify the remaining cohomogeneities up to n ´1, it remains to consider those actions that are non-polar. While the quotient spaces of polar actions on manifolds of positive curvature necessarily have boundary by work of Wilking [89], a result later generalized to singular Riemannian foliations by Corro and Moreno [15], the quotient spaces of non-polar actions may or may not have boundary. 4.2.…”

Section: Small Quotient Spacementioning

confidence: 99%

Symmetries of Spaces with Lower Curvature Bounds

Searle¹

2023

Preprint

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Core reduction for singular Riemannian foliations and applications to positive curvature

Cited by 2 publications

References 17 publications

Yamabe problem in the presence of singular Riemannian Foliations

Yamabe problem in the presence of singular Riemannian Foliations

Symmetries of Spaces with Lower Curvature Bounds

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