Core reduction for singular Riemannian foliations and applications to positive curvature

Corro, Diego and Moreno, Adam 2022. Core reduction for singular Riemannian foliations and applications to positive curvature. Annals of Global Analysis and Geometry 62 (3) , 617–634. 10.1007/s10455-022-09856-y

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Abstract

We expand upon the notion of a pre-section for a singular Riemannian foliation (M,F) , i.e. a proper submanifold N⊂M retaining all the transverse geometry of the foliation. This generalization of a polar foliation provides a similar reduction, allowing one to recognize certain geometric or topological properties of (M,F) and the leaf space M/F . In particular, we show that if a foliated manifold M has positive sectional curvature and contains a non-trivial pre-section, then the leaf space M/F has nonempty boundary. We recover as corollaries the known result for the special case of polar foliations as well as the well-known analogue for isometric group actions.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	0232-704X
Date of First Compliant Deposit:	25 October 2023
Date of Acceptance:	3 June 2022
Last Modified:	15 Nov 2024 02:45
URI:	https://orca.cardiff.ac.uk/id/eprint/162207

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