Riemannian submersions from simple, compact Lie groups

2009/10/22 by Martin Kerin, Kerin, Martin, Krishnan Shankar +1 · 1 citation
Mathematics · Physics and Astronomy · #53C20 #53C30 #57S15 #57S25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C20 #msc:53C30 #msc:57S15 #msc:57S25

paper · pdf · doi:10.48550/arxiv.0910.4344

16 pages. Dedicated to J.-H. Eschenburg on the occasion of his 60th birthday

arxiv created 2009/10/22 · openalex publication_date 2009/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group G with bi-invariant metric onto a smooth manifold that cannot be a quotient of G by a group action. This partially addresses a question of K. Grove's about Riemannian submersions from Lie groups.

Citations

• Examples of Riemannian Manifolds with non-negative sectional curvature

Cited by

• Manifold submetries from compact homogeneous spaces

Related

• Totally Geodesic Riemannian Foliations on Compact Lie Groups
• Flats in Riemannian Submersions from Lie Groups
• Existence of isometric immersions into nilpotent Lie groups
• Totally Geodesic Foliations and Doubly Ruled Surfaces in a Compact Lie Group
• Smoothness of submetries