Benci, V.; Fortunato, D.; Giannoni, F. On the existence of multiple geodesics in static space-times. (English) Zbl 0716.53057 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 8, No. 1, 79-102 (1991). The authors study geodesics in a static Lorentz-manifold (\({\mathfrak M},g)=({\mathfrak M}_ 0\times {\mathbb{R}},<.,.>\oplus (-\beta)\cdot dt^ 2)\) such that (\({\mathfrak M}_ 0,<.,.>)\) is complete and \(\beta\) is bounded and bounded away from 0. They show that (M,g) is geodesically connected and estimate the number of timelike geodesics (resp. all geodesics) which connect two given points. They derive similar results for the “T- periodic” case, in which geodesics of the form \(\gamma =(x,t)\), \(x(0)=x(T)\), \(t(0)=0\), \(t(1)=T\), \(x'(0)=x'(1)\), \(t'(0)=t'(1)\) are considered. In particular, they derive that for each \(m\in {\mathbb{N}}\) and each \(Q\in {\mathfrak M}_ 0\) there exist m different T-periodic timelike geodesics passing through (Q,0) and (Q,T), provided T is large enough and (\({\mathfrak M},g)\) is asymptotically flat in a certain sense. Reviewer: M.Kriele Cited in 45 Documents MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C22 Geodesics in global differential geometry 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces Keywords:static space-time; Lorentz metrics; critical point theory; asymptotically flat spacetimes; geodesics PDFBibTeX XMLCite \textit{V. Benci} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 8, No. 1, 79--102 (1991; Zbl 0716.53057) Full Text: DOI Numdam EuDML References: [1] Alber, S. I., The topology of functional manifolds and the calculus of variations in the large, Russian Math. 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