C . L . Terng

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An isometric action of a compact Lie group G on a Riemannian manifold M is called polar if there exists a closed, connected submanifold ∑ of M that meets all G-orbits and meets orthogonally. Such a ∑ is called a section. A section is automatically totally geodesic in M , and if it is also flat in the induced metric then the action is called hyperpolar . In(More)
The classical local invariants of a submanifold in a space form are the first fundamental form, the shape operators and the induced normal connection, and they determine the submanifold up to ambient isometry. One of the main topics in differential geometry is to study the relation between the local invariants and the global geometry and topology of(More)
A closed, connected, k-dimensional submanifold of a compact Riemannian manifold M is called a k-flat of M if it is flat in the induced metric and totally geodesic. We call M “k-flat homogeneous” if every geodesic lies in some k-flat of M , and if the group of isometries of M acts transitively on pairs (σ, p) consisting of a k-flat σ and a point p ∈ σ. An(More)
Restrictions are given on the possible marked Dynkin diagrams of isoparametric submanifolds, and their homology and cohomology are computed by an extension of the techniques used by Bott and Samelson [Bott, R. & Samelson, H. (1958) Am. J. Math. 80, 964-1029] and by Borel [Borel, A. (1953) Ann. Math. 57 (2), 115-207] for G/T.
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