Special isoparametric orbits in Riemannian symmetric spaces
ABSTRACT In the present paper orbits of isotropy subgroups in Riemannian symmetric spaces are discussed. Principal orbits of an isotropy subgroup are isoparametric in the sense of Palais and Terng (seeCritical Point Theory and Submanifold Geometry, Springer-Verlag, Berlin, 1988). We show that excepting some special cases, the shape operator with respect to the radial unit vector field determines a totally geodesic foliation on a given principal orbit. Furthermore, we prove that the shape operators and the curvature endomorphisms with respect to the normal vectors commute on these isoparametric submanifolds.
- SourceAvailable from: Richard S. Palais
Article: A General Theory of Canonical FormsTransactions of The American Mathematical Society - TRANS AMER MATH SOC. 01/1987; 300(2):771-771.
- Journal of differential geometry 01/1985; 21(1985). · 1.18 Impact Factor