<p>We show that Hadamard spaces with geometric group actions admit affine maps that are not dilations, if and only if they are Riemannian symmetric spaces of higher rank, Euclidean buildings of higher rank, or split as non-trivial metric products.</p>

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Characterization of higher rank via affine maps

  • David Lenze

摘要

We show that Hadamard spaces with geometric group actions admit affine maps that are not dilations, if and only if they are Riemannian symmetric spaces of higher rank, Euclidean buildings of higher rank, or split as non-trivial metric products.