A COMPARISON THEOREM FOR EQUIVARIANT ISOMETRIC IMMERSIONS

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Abstract

Let M and N be complete Riemannian manifolds with non-positive curvature, G be a connected Lie group acting isometrically and non-trivially on M and N. We prove that if M admits a G-equivariant isometric immersion into N, then sup KM≥KN, where KM and KNdenote the sectional curvatures of M and N respectively. The proof is based on some Rauch type comparison theorems.

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