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Spaces of Riemannian metrics on open manifolds

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Abstract

We define for the set M of metrics on an open manifold M n suitable uniform structures, obtain completed spaces b,m M or M r(I, B k ), respectively and calculate for each component of M r(I, B k ) the infinitedimensional geometry. In particular, we show that the sectional curvature is non positive.

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  1. Fachbereich Mathematik Jahnstra\e 15a, 17487, Greifswald, Germany

    Jürgen Eichhorn

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  1. Jürgen Eichhorn
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Dedicated to Katsurni Nomizu on the occasion of his 70th birthday

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Eichhorn, J. Spaces of Riemannian metrics on open manifolds. Results. Math. 27, 256–283 (1995). https://doi.org/10.1007/BF03322831

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