A note on static spaces and related problems
110 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/bb234bc7c4ec97a6d2bd6b218a8e63cf6078118f
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- On static three-manifolds with positive scalar curvature (2015, background): “It may be interesting to compare the computations carried out in this section and in the following one with the more general computations related to conformal flatness of [50].”
- Bach-Flat Critical Metrics of the Volume Functional on 4-Dimensional Manifolds with Boundary (2014, result): “We point out that some of these calculations above was also done in [4] and [23] in a different context to study the CPE Conjecture posed in “Besse book” (cf.”