Deformation of the Weighted Scalar Curvature

Pak Tung Ho   ; Jinwoo Shin

Symmetry, integrability and geometry: methods and applications, Tome 19 (2023)

Résumé

Inspired by the work of Fischer–Marsden [Duke Math. J. 42 (1975), 519–547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space, and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces.

Détail

Keywords: weighted scalar curvature, smooth metric measure space, vacuum static space.

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