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Michel, Rene

Sur quelques problèmes de géométrie globale des geodesiques. (French) Zbl 0415.53031

Bol. Soc. Bras. Mat. 9, No. 2, 19-37 (1978).
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Cited in 7 Documents

MSC:

53C22 Geodesics in global differential geometry
53C65 Integral geometry
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions

Keywords:

geodesics without conjugate points; rigidity situation; unit bundle; Riemannian geometry; closed geodesic

Citations:

Zbl 0030.07901; Zbl 0116.135; Zbl 0265.53041; Zbl 0346.50031
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\textit{R. Michel}, Bol. Soc. Bras. Mat. 9, No. 2, 19--37 (1978; Zbl 0415.53031)
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References:

[1] E. HOPF,Closed surfaces without conjugate points, Proc. Nat. Ac. Sci. U.S.A. 34, 1948. · Zbl 0030.07901
[2] L. W. GREEN,Auf Wiedersehensflächen, Ann. of Maths. Vol. 78 n.o 2 1963.
[3] R. MICHEL,Comptes Rendus Acad. Sc. Paris, t 284 serie A-183, 1977.
[4] M. BERGER,Lectures on Geodesics in Riemannian Geometry, Tata Institute of Fund. Research, Bombay, 1965.
[5] A. BESSE,Manifolds all of whose geodesics are closed Ergebnisse der Mathematik, Band 93, Springer. · Zbl 0387.53010
[6] C. GODBILLON,Géométrie Differentielle et Mécanique Analytique, 1969, Hermann, Paris.
[7] J. DIEUDONNÉ,Elements d’ analyse, vol. 3, 1970, Gauthier-Villars, Paris.
[8] W. GREUB, S. HALPERIN, R. VANSTONE,Connections, Curvature and Cohomology, Ac. Press, Vol. I, 1972. · Zbl 0322.58001
[9] S. S. CHERN (Editor),Studies in Global Geometry and Analysis, Math. Assoc. of America, prentice Hall, 1967.
[10] M. BERGER, Comptes Rendus Acad. Sc. Paris, t. 284–serie A–1221, 1977.
[11] L. GREEN,A théorème of E. Hopf, Michigan J. of Math. (vol. 5) 1958.
[12] A. AVEZ, Comptes Rendus Acad. Sc. Paris, t. 270–serie A, 1970.
[13] R. MICHEL, Bull. S.M.F., 101, 1973.
[14] R. MICHEL, Journal de Math. Pures et Appliquées, 53, 1974.
[15] I.M. GELFAND, M.I. GRAEV, Z.Ya. SHAPIRO, Funct. Anal., 3, n.o 2, 1969.
[16] R. MICHEL,Tenseurs symétriques et Géodésiques, Comptes Rendus Acad. SC. Paris t. 284 serie A, 1065.
[17] D. LAUGWITZ,Differential and Riemannian Geometry, Academic Press, 1965.
[18] A. WEINSTEIN,On the volume of manifolds all of whose geodesics are closed, J. of Differential Geometry, 9, 1974. · Zbl 0289.53032
[19] H. WEYL,On the volume of tubes, Am. J. of Math. 61, 1939. · Zbl 0021.35503
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.