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≥ inf KN, where KM and KN denote the sectional curvatures of M and N respectively. The proof is based on some Rauch type comparison theorems.
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Csikós, B. A Comparison Theorem for Equivariant Isometric Immersions. Periodica Mathematica Hungarica 36, 97–103 (1998). https://doi.org/10.1023/A:1004673507600
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DOI: https://doi.org/10.1023/A:1004673507600