20 jun 2023 -- 16:00
Dipartimento di Matematica "G. Peano", Università di Torino
Differential Geometry Seminar Torino
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 talk, we give a necessary and sufficient condition for a CPE metric to be Einstein in terms 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.