Tohoku Mathematical Journal

Closed geodesics on certain Riemannian manifolds of positive curvature

Yôtarô Tsukamoto

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 18, Number 2 (1966), 138-143.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178243444

Digital Object Identifier
doi:10.2748/tmj/1178243444

Mathematical Reviews number (MathSciNet)
MR0203652

Zentralblatt MATH identifier
0145.18503

Subjects
Primary: 53.72

Citation

Tsukamoto, Yôtarô. Closed geodesics on certain Riemannian manifolds of positive curvature. Tohoku Math. J. (2) 18 (1966), no. 2, 138--143. doi:10.2748/tmj/1178243444. https://projecteuclid.org/euclid.tmj/1178243444.


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References

  • [1] M. BERGER, Les varietes riemanniennes a courbure positive, Bull. Soc. Math. Belgique, 10(1958), 89-104.
  • [2] M. BERGER, Sur quelques varietes riemanniennes suffsamment pinceeb, Bull. Soc. Math France, 88(1960), 57-71.
  • [3] M. BERGER, Les varietes riemanniennes --r- pincees, Ann. Scula Nor. Sup. Pisa, 14(1960), 161-170.
  • [4] W. KLINGENBERG, Contributions to Riemannian geometry in the large, Ann. Math., 69(1959), 654-666.
  • [5] W. KLINGENBERG, Neue Ergebnisse iiber konvexe Flachen, Comm. Math. Helv., 34(1960), 17-36.
  • [6] W. KLINGENBERG, Uber Riemannsche Mannigfaltigkeiten mit positiver Kriimmung, Comm. Math. Helv., 35(1961), 47-54.
  • [7] W. KLINGENBERG, Riemannsche Geometric im Grossen, Lecture note, Bonn Univ., (1962)
  • [8] S. B. MYERS, Riemannian manifolds in the large, Duke Math. Journ., 1(1935), 39-49
  • [9] H. E. RAUCH, A contributionto differential geometry in the large, Ann. Math., 54(1951), 38-51.
  • [10] V. A. TOPONOGOV, Riemannian spaces which have their curvature bounded from belo by a positive number, Uspehi Nauk, 14(85) (1959), 87-130.
  • [11] V. A. TOPONOGOV, Dependence between curvature and topological structure of Riemannia spaces of even dimensions, Dok. Acad. Nauk, 133(1960), 1031-1033.
  • [12] V. A. TOPONOGOV, Estimation of length of closed geodesies on compact Riemannian space of positive curvature, Dok. Acad. Nauk, 154(1964), 1047-1049.
  • [13] Y. TSUKAMOTO. On Riemannian manifolds with positive curvature, Mem. Fac. Sci Kyushu Univ. Ser. A Math., 15(1962), 90-96.

Corrections

  • See Correction: Yôtarô Tsukamoto. Some corrections to: ``Closed geodesics on certain Riemannian manifolds of positive curvature''. Tohoku Math. J., Volume 21, Number 4 (1969), pp. 674-675.