Corank and asymptotic filling-invariants for symmetric spaces
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Let X be a Riemannian symmetric space of noncompact type. We prove that there exists an embedded submanifold \( Y \subset X \) which is quasi-isometric to a manifold with strictly negative sectional curvature, which intersects a given flat F in a geodesic line and which satisfies dim(Y) — 1 = dim(X) — rank(X). This yields an estimate of the hyperbolic corank of X. As another application we show that certain asymptotic filling invariants of X are exponential.
KeywordsSymmetric Space Sectional Curvature Geodesic Line Riemannian Symmetric Space Noncompact Type
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