Geodesic
Regular and Quasiregular Isometric Flows on Riemannian Manifolds
Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 3-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the nontrivial Killing vector fields of constant length and the corresponding flows on smooth Riemannian manifolds. We describe the properties of the set of all points of finite (infinite) period for general isometric flows on Riemannian manifolds. It is shown that this flow is generated by an effective almost free isometric action of the group $S^1$ if there are no points of infinite or zero period. In the last case, the set of periods is at most countable and generates naturally an invariant stratification with closed totally geodesic strata; the union of all regular orbits is an open connected dense subset of full measure. 
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V. N. Berestovskii; Yu. G. Nikonorov. Regular and Quasiregular Isometric Flows on Riemannian Manifolds. Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 3-18. http://geodesic.mathdoc.fr/item/MT_2007_10_2_a0/

[1] Besse A., Mnogoobraziya s zamknutymi geodezicheskimi, Mir, M., 1981 | MR

[2] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, t. I, II, Nauka, M., 1981

[3] Khelgason S., Differentsialnaya geometriya i simmetricheskie prostranstva, Mir, M., 1964 | Zbl

[4] Eizenkhart L. P., Rimanova geometriya, Izd-vo inostr. lit., M., 1948

[5] Epstein D. B. A., “Periodic flows on three-manifolds”, Ann. of Math., 95:1 (1972), 68–82 | DOI | MR

[6] Epstein D. B. A. and Vogt E., “A counterexample to the periodic orbit conjecture in codimension 3”, Ann. of Math., 108:3 (1978), 539–552 | DOI | MR | Zbl

[7] Kobayashi S., “Fixed points of isometries”, Nagoya Math. J., 13 (1958), 63–68 | MR | Zbl

[8] Ozols V., “Periodic orbits of isometric flows”, Nagoya Math. J., 48 (1972), 160–172 | MR

[9] Sullivan D., “A counterexample to the periodic orbit conjecture”, Inst. Hautes Études Sci. Publ. Math., 46 (1976), 5–14 | DOI | MR | Zbl

[10] Sullivan D., “A foliation of geodesics is characterized by having no “tangent homologies””, J. Pure Appl. Algebra, 13:1 (1978), 101–104 | DOI | MR | Zbl

[11] Wadsley A. W., “Geodesic foliations by circles”, J. Diff. Geom., 10:4 (1975), 541–549 | MR | Zbl