On local isometric immersions of Riemannian symmetric spaces. (English) Zbl 0533.53052

Agaoka, Yoshio; Kaneda, Eiji

Tôhoku Math. J., II. Ser. 36, 107-140 (1984).

Let \(M=G/K\) be an s.c. irreducible Riemannian symmetric space of compact type. Let 2c(M) denote the maximal rank of its curvature transformation. Then c(M) and c(M)-2 are lower bounds for the codimension of isometric and conformal immersions of M into Euclidean space. c(M) is computed for all M. For example, \(2c(M)=\dim M-rkG+rkK\), if M is not a real Grassmannian.

Reviewer: D.Ferus

MSC:

53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C35	Differential geometry of symmetric spaces

Keywords:

isometric immersion; conformal immersion; Riemannian symmetric space; maximal rank

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