Proper actions of high-dimensional groups on complex manifolds

A. V. Isaev*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently high, all proper effective actions can be explicitly determined, and our principal goal is to provide a comprehensive exposition of known classification results in the complex setting. They include a complete description of Kobayashi-hyperbolic manifolds with high-dimensional automorphism group, which is a case of special interest.

    Original languageEnglish
    Pages (from-to)251-285
    Number of pages35
    JournalBulletin of Mathematical Sciences
    Volume5
    Issue number2
    DOIs
    Publication statusPublished - 1 Jan 2015

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