Abstract
Characterisation of 2-dimensional Riemannian manifolds (M, g) (in particular, of surfaces with constant gaussian curvatureK=1/c 2, o,−1/c 2, respectively) whose tangent circle bundle (T cM, gs) (g s=Sasaki metric) admit an «almost-regular» vector field belonging to an eigenspace of the Ricci operator.
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Abraham R., Marsden J. E.,Foundations of Mechanics, Benjamin, Second Edition, London, 1978.
Avez A., Buzzanca C.,Flusso geodetico sul fibrato unitario tangente di una superficie, Rend. Circolo Mat. Palermo II,25 (1976), 176–182.
Berger M., Gauduchon P., Mazet E.,Le spectre d'une variété riemannienne, Lecture Notes Vol. 194, Berlin-Heidelberg-New York: Springer, 1971.
Besse A.,Manifolds all of whose geodesics are closed, Springer-Verlag, 1978.
Buzzanca C.,Courbure de Ricci et géométrie conforme, Ann. di Mat. Pura ed Appl. (à paraître).
Buzzanca C.,Actions de groupes, opérateurs différentiels et mécanique sur certains fibrés riemanniens III (preprint).
Grimaldi R.,Curvatura di Ricci e proprietà spettrali del fibrato sferico tangente delle superfici, Rend. Sem. Mat. Univers. Politec. Torino, Vol. 40°,2 (1982), 167–174.
Lichnerowicz A.,Géométrie des groupes de transformations, Dunod, Paris, 1958.
Milnor J.,Morse Theory, Annals of Math. Studies 51, Princeton: Princeton University Press 1962.
Pham Mau Quan,Géométrie du problème de Kepler: courbure et géodésiques. C. R. Acad. Sciences, Paris, A,291, (1980) 219–221.
Pham Mau Quan,Géométrie du problème de Kepler: orbites et variétés des orbites. C. R. Acad. Sciences, Paris, A,291, (1980) 299–302.
Sasaki S.On the differential geometry of tangent bundles of riemannian manifold II, Tôhoku Math. Journal,14 (1962), 146–155.
Tanno S.Killing vectors and geodesic flow vectors on tangent bundles, J. Reine Angew. Math.282 (1976), 162–171.
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Buzzanca, C. Actions de IR et courbure de ricci du Fibré unitaire tangent des surfaces. Rend. Circ. Mat. Palermo 35, 244–260 (1986). https://doi.org/10.1007/BF02844735
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DOI: https://doi.org/10.1007/BF02844735