Skip to main content
eScholarship
Open Access Publications from the University of California

A note on static spaces and related problems

  • Author(s): Qing, J
  • Yuan, W
  • et al.
Abstract

In this paper we study static spaces introduced in Hawking and Ellis (1975) [1], Fischer and Marsden (1975) [3] and Riemannian manifolds possessing solutions to the critical point equation introduced in Besse (1987) [11], Hwang (2000) [12]. In both cases, on the manifolds there is a function satisfying a particular Ricci-Hessian type equation (1.6). With an idea similar to that used in Cao et al. (2012) [15,16], we have made progress in solving the problem raised in Fischer and Marsden (1975) [3] of classifying vacuum static spaces and in proving the conjecture proposed in Besse (1987) [11] concerning manifolds admitting solutions to the critical point equation in general dimensions. We obtain even stronger results in dimension 3. © 2013 Elsevier B.V.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View