Minimal orbits of metrics

[摘要] The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian metrics with its L-2 metric. Following Arnaudon and Paycha (1995) and Maeda, Rosenbeg 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 fmd a flat 2-torus giving a stable minimal orbit. We prove that isolated orbits are minimal, as in finite dimensions.

[发布日期] 1997-11-01

[关键词] Riemannian geometry;orbits of metrics