Tanaka, Minoru Invariant closed geodesics under isometries of prime power order. (English) Zbl 0426.58007 Kōdai Math. Semin. Rep. 29, 120-129 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable) 53C22 Geodesics in global differential geometry 53C20 Global Riemannian geometry, including pinching Keywords:isometry-invariant geodesic equivariant degenerate Morse theory; index; nullity; characteristic invariant Citations:Zbl 0297.58006; Zbl 0364.58014; Zbl 0203.544; Zbl 0325.58010; Zbl 0375.58010 PDFBibTeX XMLCite \textit{M. Tanaka}, Kōdai Math. Semin. Rep. 29, 120--129 (1977; Zbl 0426.58007) Full Text: DOI References: [1] R. BOTT, On the iteration of closed geodesies and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171-206. · Zbl 0074.17202 · doi:10.1002/cpa.3160090204 [2] D. GROMOLL AND W. MEYER, On differentiate functions with isolated criti cal points, Topology 8 (1969), 361-369. · Zbl 0212.28903 · doi:10.1016/0040-9383(69)90022-6 [3] D. GROMOLL AND W. MEYEE, Periodic geodesies on compact Riemannian ma nifolds, J. differential Geometry 3 (1969), 493-510. · Zbl 0203.54401 [4] K. GROVE, Condition (C) for the energy integral on certain path spaces an applications to the theory of geodesies, J. Differential Geometry 8 (1973), 207-223. · Zbl 0277.58004 [5] K. GROVE, Isometry-invariant geodesies, Topology 13 (1974), 281-292 · Zbl 0289.58007 · doi:10.1016/0040-9383(74)90021-4 [6] K. GROVE, Involutive-invariant geodesies, Math. Scand. 36 (1975), 97-108 · Zbl 0297.58006 [7] M. MORSE, The calculus of variations in the large, Amer. Math. Soc. Colloq Publ. vol. 18, (1934). · Zbl 0011.02802 [8] J. P. SERRE, Homologie singuliere des espaces fibres, Ann. of Math. 54 (1951), 425-505 · Zbl 0045.26003 · doi:10.2307/1969485 [9] M. TANAKA, On invariant closed geodesies under isometries, to appear i Kdai Math. Sem. Rep. · Zbl 0364.58014 · doi:10.2996/kmj/1138847446 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.