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Einstein-type structures, Besse's conjecture and a uniqueness result for a $varphi$-CPE metric in its conformal class | | Giulio Colombo
; Luciano Mari
; Marco Rigoli
; | | Date: |
2 Jan 2022 | | Abstract: | In this paper, we study an extension of the CPE conjecture to manifolds $M$
which support a structure relating curvature to the geometry of a smooth map
$varphi : M o N$. The resulting system, denoted by $(varphi-mathrm{CPE})$,
is natural from the variational viewpoint and describes stationary points for
the integrated $varphi$-scalar curvature functional restricted to metrics with
unit volume and constant $varphi$-scalar curvature. We prove both a rigidity
statement for solutions to $(varphi-mathrm{CPE})$ in a conformal class, and a
gap theorem characterizing the round sphere among manifolds supporting
$(varphi-mathrm{CPE})$ with $varphi$ a harmonic map. | | Source: | arXiv, 2201.00263 | | Services: | Forum | Review | PDF | Favorites | |
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