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Ziller, Wolfgang

The free loop space of globally symmetric spaces. (English) Zbl 0338.58007

Invent. Math. 41, 1-22 (1977).
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Cited in 36 Documents

MSC:

58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
53C35 Differential geometry of symmetric spaces
57N65 Algebraic topology of manifolds
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References:

[1] Araki, S.: On Bott-SamelsonK-cycles associated with a symmetric space. J. of Math. Osaka University13, 87-133 (1962)
[2] Borel, A.: Sur la cohomologie des espaces fibres principaux et des espaces homogenes. Ann. of Math.57, 115-207 (1953) · Zbl 0052.40001 · doi:10.2307/1969728
[3] Borel, A., Hirzebruch, F.: Characteristic classes and homogeneous spaces I. Am. J. of Math.80, 459-538 (1958) · Zbl 0097.36401 · doi:10.2307/2372795
[4] Bott, R., Samelson, H.: Applications of Morse theory to symmetric spaces. Am. J. of Math.80, 964-1029 (1958) · Zbl 0101.39702 · doi:10.2307/2372843
[5] Bott, R.: The stable homotopy of the classical groups. Ann. of Math.70, 313-337 · Zbl 0129.15601
[6] Eliasson, H.: Morse theory for closed curves. In: Symp for inf. dim. Topology, Lousiana State University. Ann. of Math. Studies No. 69, 63-77. Princeton University Press 1972
[7] Eliasson, H.: Über die Anzahl geschlossener Geodätischer in gewissen Riemannschen Mannigfaltigkeiten. Math. Ann.166, 119-147 (1966) · Zbl 0145.42303 · doi:10.1007/BF01361443
[8] Flaschel, P., Klingenberg, W.: Riemannsche Hilbertmannigfaltigkeiten Periodische Geodätische. Lecture Notes in Math. 282. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0238.58009
[9] Gromoll, D., Meyer, W.: Periodic geodesics on compact riemannian manifolds. J. of Diff. Geom.3, 493-510 (1969) · Zbl 0203.54401
[10] Klein, P.: Über die Kohomologie des freien Schleifenraumes. Bonner Math. Schriften 55. Bonn: Math. Institut 1972 · Zbl 0248.55011
[11] Klingenberg, W.: The space of closed curves on the sphere. Topology7, 395-415 (1968) · Zbl 0174.55102 · doi:10.1016/0040-9383(68)90015-3
[12] Klingenberg, W.: The space of closed curves on a projective space. Quart. J. Math. Oxford Ser. 20 No. 77, 11-31 (1969) · Zbl 0177.26202 · doi:10.1093/qmath/20.1.11
[13] Klingenberg, W.: Lectures on closed geodesics. Preprint Bonn 1975 · Zbl 0397.58018
[14] Loos, O.: Symmetric spaces II. New York: Benjamin 1969 · Zbl 0175.48601
[15] ?varc, A.S.: Homology of the space of closed curves. Trudy Moscow. Mat. Obsc.9, 3-44 (1960)
[16] Vigué, M., Sullivan, D.: The homology theory of the closed geodesic problem. Preprint Orsay and bures-sur-Yvette, 1975. To appear in J. of Diff. Geom.
[17] Wolf, J.A.: Spaces of constant curvature. New York-Toronto-London: McGraw-Hill 1967 · Zbl 0162.53304
[18] Ziller, W.: Geschlossene Geodätische auf global symmetrischen und homogenen Räumen. Dissertation, Bonn 1975 · Zbl 0343.53032
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