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- W3113020111 abstract "We call CPE metrics the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume. In this short note, we give a necessary and sufficient condition for a CPE metric to be Einstein in therms of $sigma_2$-singular spaces. Such a result improves our understanding about CPE metrics and Besse's conjecture with a new geometric point of view. Moreover, we prove that the CPE condition can be replaced by the related vacuum static space condition to characterize closed Einstein manifolds in terms of $sigma_2$-singular spaces." @default.
- W3113020111 created "2020-12-21" @default.
- W3113020111 creator A5001188507 @default.
- W3113020111 date "2020-02-09" @default.
- W3113020111 modified "2023-09-27" @default.
- W3113020111 title "On the interplay between CPE metrics, vacuum static spaces and $sigma_2$-singular spaces" @default.
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