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One class of n-dimensional manifolds with closed geodesics

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Literature cited

  1. 1.

    O. Zoll, “Über Flächen mit Scharen geschlossener geodätischer Linien,” Math. Ann.,57, 108–133 (1903).

  2. 2.

    A. Besse, Manifolds All of Whose Geodesies are Closed, Springer-Verlag, Berlin-New York (1978).

  3. 3.

    V. N. Kolokol'tsov, “New examples of manifolds with closed geodesies,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 4, 80–82 (1984).

  4. 4.

    V. N. Kolokol'tsov, SC-Geodesic Flows on a Sphere with an Additional Integral That Is Quadratic with Respect to Velocities [in Russian], Moscow (1984). Manuscript deposited in VINITI on August 20, 1984. No. 5924.

  5. 5.

    A. I. Lur'e, Analytical Mechanics [in Russian], Gos. Izdat. Fiz.-Mat. Lit., Moscow (1961).

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Translated from Ukrainskii Geometricheskii Sbornik, No. 31, pp. 90–100, 1988.

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Lisitsa, V.T. One class of n-dimensional manifolds with closed geodesics. J Math Sci 54, 728–735 (1991). https://doi.org/10.1007/BF01097420

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  • Manifold
  • Closed Geodesic