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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
