Publications [#243382] of Robert Bryant

Papers Published

1. Bryant, RL, Bochner-Kahler metrics, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 14 no. 3 (January, 2001), pp. 623-715, AMER MATHEMATICAL SOC [MR2002i:53096], [math.DG/0003099], [doi]
   (last updated on 2025/03/31)

   Abstract:
   A Kahler metric is said to be Bochner-Kahler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least 2. In this article it will be shown that, in a certain well- defined sense, the space of Bochner-Kahler metrics in complex dimension n has real dimension n+1 and a recipe for an explicit formula for any Bochner-Kahler metric is given. It is shown that any Bochner-Kahler metric in complex dimension n has local (real) cohomogeneity at most~n. The Bochner-Kahler metrics that can be `analytically continued' to a complete metric, free of singularities, are identified. In particular, it is shown that the only compact Bochner- Kahler manifolds are the discrete quotients of the known symmetric examples. However, there are compact Bochner- Kahler orbifolds that are not locally symmetric. In fact, every weighted projective space carries a Bochner-Kahler metric. The fundamental technique is to construct a canonical infinitesimal torus action on a Bochner-Kahler metric whose associated momentum mapping has the orbits of its symmetry pseudo-groupoid as fibers.