Chapter Eight. Lorentz Geometry and Harmonic Vector Fields
Chapter 8 is devoted to the study of harmonic vector fields on semi-Riemannian manifolds with an emphasis on the Lorentzian case. We derive the first variation formula for the spacelike energy following the work by O. Gil-Medrano & A. Hurtado (2004). Several explicit examples are considered, including rigid irrotational reference frames on Fefferman spaces. The second variation formula for the spacelike energy is derived and applied to stability questions. In particular, Chapter 8 reports ...

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