Abstract
We prove that for any compact manifold of dimension \(>\)1, the set of pseudo-Riemannian metrics having a trivial isometry group contains an open and dense subset of the space of metrics.
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References
Beig, R., Chruściel, P., Schoen, R.: KIDs are non-generic. Ann. Henri Poincaré 6(1), 155–194 (2005)
D’Ambra, G., Gromov, M.: Lectures on transformation groups: geometry and dynamics. Surv. Differ. Geometry (supplement to the J. Differ. Geometry) 1, 19–111 (1991)
Ebin, D.: The manifold of Riemannian metrics. In: 1970 Global Analysis (Proc. Sympos. Pure Math., vol. XV, Berkeley, Calif., 1968), pp. 11–40, Am. Math. Soc., Providence (1970)
Kim, Y.W.: Semicontinuity of compact group actions on compact differentiable manifolds. Arch. Math. (Basel) 49(5), 450–455 (1987)
Mounoud, P.: Dynamical properties of the space of Lorentzian metrics. Comment. Math. Helv. 78(3), 463–485 (2003)
Zeghib, A.: Isometry groups and geodesic foliations of Lorentz manifold. Part I: foundations of Lorentz dynamics. Geom. Funct. Anal. 9(4), 775–822 (1999)
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Communicated by A. Constantin.
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Mounoud, P. Metrics without isometries are generic. Monatsh Math 176, 603–606 (2015). https://doi.org/10.1007/s00605-014-0614-6
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DOI: https://doi.org/10.1007/s00605-014-0614-6