Addendum to “Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric” [Ann. I. H. Poincaré – AN 27 (3) (2010) 857–876]
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 5, p. 961-968

We give the details of the proof of equality (29) in Caponio et al. (2010) [3].

On donne les détails de la preuve de lʼéquation (29) dans Caponio et al. (2010) [3].

DOI : https://doi.org/10.1016/j.anihpc.2013.03.005
Classification:  58E05,  53C60,  53C22
Keywords: Morse theory, Critical groups, Finsler metrics
@article{AIHPC_2013__30_5_961_0,
     author = {Caponio, Erasmo and Javaloyes, Miguel \'Angel and Masiello, Antonio},
     title = {Addendum to ``Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric'' [Ann. I. H. Poincar\'e -- AN 27 (3) (2010) 857--876]},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {30},
     number = {5},
     year = {2013},
     pages = {961-968},
     doi = {10.1016/j.anihpc.2013.03.005},
     zbl = {1286.58007},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2013__30_5_961_0}
}
Caponio, Erasmo; Javaloyes, Miguel Ángel; Masiello, Antonio. Addendum to “Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric” [Ann. I. H. Poincaré – AN 27 (3) (2010) 857–876]. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 5, pp. 961-968. doi : 10.1016/j.anihpc.2013.03.005. http://www.numdam.org/item/AIHPC_2013__30_5_961_0/

[1] A. Abbondandolo, M. Schwarz, A smooth pseudo-gradient for the Lagrangian action functional, Adv. Nonlinear Stud. 9 (2009), 597-623 | Zbl 1185.37145

[2] E. Caponio, M.A. Javaloyes, A. Masiello, On the energy functional on Finsler manifolds and applications to stationary spacetimes, Math. Ann. 351 (2011), 365-392 | Zbl 1228.53052

[3] E. Caponio, M.A. Javaloyes, A. Masiello, Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 857-876 | Numdam | Zbl 1196.58005

[4] K.-C. Chang, A variant mountain pass lemma, Sci. Sinica Ser. A 26 (1983), 1241-1255 | Zbl 0544.35044

[5] K.-C. Chang, Infinite-Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, MA (1993)

[6] K.-C. Chang, H 1 versus C 1 isolated critical points, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 441-446 | Zbl 0810.35025

[7] M. Crampin, The Morse index theorem for general end conditions, Houston J. Math. 27 (2001), 807-821 | Zbl 1007.58008

[8] M.P. Do Carmo, Riemannian Geometry, Birkhäuser, Boston, MA (1992)

[9] S. Lang, Differential and Riemannian Manifolds, Grad. Texts in Math., Springer-Verlag, New York (1995) | Zbl 0824.58003

[10] C. Li, S. Li, J. Liu, Splitting theorem, Poincaré–Hopf theorem and jumping nonlinear problems, J. Funct. Anal. 221 (2005), 439-455 | Zbl 1129.35392

[11] J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Appl. Math. Sci., Springer-Verlag, New York (1989) | Zbl 0676.58017

[12] R.S. Palais, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966), 1-16 | Zbl 0138.18302

[13] E.H. Rothe, Morse theory in Hilbert space, Rocky Mountain J. Math. 3 (1973), 251-274 | Zbl 0281.49027