Minimal orbits of metrics

Yoshiaki Maeda, Steven Rosenberg, Philippe Tondeur

Research output: Contribution to journalArticlepeer-review

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
Externally publishedYes

Keywords

  • Orbits of metrics
  • Riemannian geometry

ASJC Scopus subject areas

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

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