Tight Equivariant Immersions of Symmetric Spaces
نویسندگان
چکیده
Introduction. Let G/K be a compact, irreducible symmetric space and Q = f+p the Lie algebra of G. If ir is a non trivial real class-one representation of G on E with O^e, infixed, then the map TlG/K —*E given by gK—*ir{g)e gives an immersion of G/K into E. The purpose of this note is to announce the classification of such immersions with minimal absolute curvature (i.e., are tight) [ l ] , [4]. In a slightly different vein is the problem of finding to what symmetric spaces can the work of Frankel [2] be extended. One can describe Frankel's method as "take an equivariant immersion of a homogeneous space and examine the critical manifolds for nondegenerate height functions. " The present work shows that to extend Frankel's results to spaces which are not jR-spaces, the exceptional groups for instance, will require some modification of method. The author is indebted to Professor Sigurdur Helgason for his unfailing encouragement and many useful discussions.
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