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- Title
Delaunay-Type Hypersurfaces in Cohomogeneity One Manifolds.
- Authors
Bettiol, Renato G.; Piccione, Paolo
- Abstract
Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one group actions and variational bifurcation techniques. Our construction specializes to the classical examples in round spheres, and allows to obtain Delaunay-type hypersurfaces in many other ambient spaces, ranging from complex and quaternionic projective spaces to Kervaire exotic spheres.
- Subjects
CURVATURE; CURVED surfaces; SUBMANIFOLDS; HYPERSURFACES; BIFURCATION theory; MATHEMATICAL models
- Publication
IMRN: International Mathematics Research Notices, 2016, Vol 2016, Issue 10, p3124
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnv231