We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Clifford systems, Cartan hypersurfaces and Riemannian submersions.
- Authors
Li, Qichao
- Abstract
Cartan hypersurfaces are minimal isoparametric hypersurfaces with 3 distinct constant principal curvatures in unit spheres. In this article, we firstly build a relationship between the focal submanifolds of Cartan hypersurfaces and the Hopf fiberations and give a new proof of the classification result on Cartan hypersurfaces. Nextly, we show that there exists a Riemannian submersion with totally geodesic fibers from each Cartan hypersurface M to the projective planes $${{\mathbb{F}}P^2}$$ ( $${{\mathbb{F}}={\mathbb{R}},{\mathbb{C}},{\mathbb{H}},{\mathbb{O}}}$$ for m = 1, 2, 4, 8, respectively) endowed with the canonical metrics. As an application, we give several interesting examples of Riemannian submersions satisfying a basic equality due to Chen (Proc Jpn Acad Ser A Math Sci 81:162-167, 2005).
- Subjects
RIEMANNIAN submersions; CLIFFORD algebras; HYPERSURFACES; SUBMANIFOLDS; HOPF algebras; MATHEMATICAL analysis
- Publication
Journal of Geometry, 2016, Vol 107, Issue 3, p557
- ISSN
0047-2468
- Publication type
Article
- DOI
10.1007/s00022-015-0287-x