Minimal orbits of metrics

Yoshiaki Maeda, Steven Rosenberg, Philippe Tondeur

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian metrics with its L2 metric. Following Arnaudon and Paycha (1995) and Maeda, Rosenberg and Tondeur (1993), we define minimal orbits for this action by a zeta function regularization. We show that odd dimensional isotropy irreducible homogeneous spaces give rise to minimal orbits, the first known examples of minimal submanifolds of infinite dimension and codimension. We also find a flat 2-torus giving a stable minimal orbit. We prove that isolated orbits are minimal, as in finite dimensions.

    Original languageEnglish
    Pages (from-to)319-349
    Number of pages31
    JournalJournal of Geometry and Physics
    Volume23
    Issue number3-4
    DOIs
    Publication statusPublished - 1997 Nov

    Keywords

    • Orbits of metrics
    • Riemannian geometry

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Geometry and Topology

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  • Cite this

    Maeda, Y., Rosenberg, S., & Tondeur, P. (1997). Minimal orbits of metrics. Journal of Geometry and Physics, 23(3-4), 319-349. https://doi.org/10.1016/S0393-0440(97)80008-3