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On focal submanifolds of isoparametric hypersurfaces and Simons formula
- Publication Year :
- 2015
-
Abstract
- The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being $\mathcal{A}$-manifolds in the sense of A.Gray but rarely Ricci-parallel (\cite{QTY},\cite{LY},\cite{TY3}). In this paper we study the geometry of the focal submanifolds via Simons formula. We show that all the focal submanifolds with $g\geq3$ are not normally flat by estimating the normal scalar curvatures. Moreover, we give a complete classification of the semiparallel submanifolds among the focal submanifolds.<br />Comment: 12 pages, all comments are welcomed
- Subjects :
- Mathematics - Differential Geometry
53A30, 53C42
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1501.07043
- Document Type :
- Working Paper