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On the Kähler geometry of the Hilbert-Schmidt Grassmannian

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Abstract

We compute the Riemann curvature tensor of the Hilbert-Schmidt Grassmannian with respect to its natural Kähler structure. The sectional curvature is shown to be non-negative. We also discuss the Kähler structure of the Hilbert-Schmidt space of almost complex structures whose sectional curvature is shown to be non-positive.

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Authors and Affiliations

  1. Ecole Polytechnique Centre de Mathematiques, Unité Associée au C.N.R.S. no 169, F-91128, Palaiseau cedex, France

    Osmo Pekonen

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  1. Osmo Pekonen
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Research supported by a grant from the Osk. Huttunen Foundation and the Wihuri Foundation (Finland).

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Pekonen, O. On the Kähler geometry of the Hilbert-Schmidt Grassmannian. Manuscripta Math 63, 21–27 (1989). https://doi.org/10.1007/BF01173699

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