Curvature Estimates for Irreducible Symmetric Spaces

Abstract

By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, this paper verifies Sampson’s conjecture in most cases for irreducible Riemannian symmetric spaces of noncompact type.

Keywords

Symmetric space / Semi-simple Lie algebra / Harmonic map / 2E60 / 53C35 / 53C43

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