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The Chern Symposium 1979 pp 23–39Cite as

Isometric Families of Kähler Structures

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Abstract

The present study is motivated by the classical problem, loosely stated, of determining and describing, for any given family of complex analytic structures on a fixed, underlying real manifold, which subfamily consists of algebraic manifolds. This problem, which is probably inaccessible in its full generality, even when correctly stated with its missing qualifications, is treated here in a very restricted case, where each of the complex structures of the families under consideration admits a Kähler metric, such that the complex manifolds of the same family are isometric (though not complex analytically, in general). Clearly, this situation is highly restrictive compared to the general problem; however the information that one can extract from the two typical classes of such isometric families that can occur provides some interesting results on the global structure of some moduli spaces of nonalgebraic varieties, such as the K3-surfaces, the complex tori, and a special type of 2n-dimensional, rational affine variety.

Supported in part by NSF grant No. MCS 78-02285.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadephia, PA, 19104, USA

    Eugenio Calabi

  2. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Eugenio Calabi

Authors
  1. Eugenio Calabi
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    W.-Y. Hsiang , S. Kobayashi , I. M. Singer , J. Wolf  & H.-H. Wu , , ,  & 

  2. Department of Mathematics, California Institute of Technology, 91125, Pasadena, CA, USA

    A. Weinstein

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© 1980 Springer-Verlag New York Inc.

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Calabi, E. (1980). Isometric Families of Kähler Structures. In: Hsiang, WY., Kobayashi, S., Singer, I.M., Wolf, J., Wu, HH., Weinstein, A. (eds) The Chern Symposium 1979. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8109-9_3

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  • DOI: https://doi.org/10.1007/978-1-4613-8109-9_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8111-2

  • Online ISBN: 978-1-4613-8109-9

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