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Integral geometry of a tensor field on a manifold whose curvature is bounded above. (English. Russian original) Zbl 0781.53057
Sib. Math. J. 33, No. 3, 524-533 (1992); translation from Sib. Mat. Zh. 33, No. 3, 192-204 (1992).

MSC:
53C65 Integral geometry
53C20 Global Riemannian geometry, including pinching
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[1] M. M. Lavrent’ev and A. L. Bukhgeim, ?On a class of operator equations of the first kind?, Funkts. Anal. Prilozhen.,7, No. 4, 44-53 (1973).
[2] L. N. Pestov and V. A. Sharafutdinov, ?Integral geometry of tensor fields on a manifold of negative curvature?, Sib. Mat. Zh.,29, No. 3, 114-130 (1i88). · Zbl 0659.53051
[3] V. A. Sharafutdinov, ?Integral geometry of tensor fields along geodesics of a metric close to the Euclidean metric?, Dokl. Akad. Nauk SSSR,304, No. 6, 1308-1311 (1989). · Zbl 0681.53040
[4] M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Moscow (1980).
[5] R. S. Palais, Seminar on the Atiyah-Singer Index Theorem, Princeton University Press, Princeton, NJ (1965). · Zbl 0137.17002
[6] R. Michel, ?Sur la rigidité imposée par la longueur des géodesiques?, Invent. Math.,65, No. 1, 71-84 (1981). · Zbl 0471.53030 · doi:10.1007/BF01389295
[7] D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen, Springer, Berlin (1968). · Zbl 0155.30701
[8] A. L. Besse, Manifolds All of Whose Geodesics are Closed, Springer, Berlin (1978). · Zbl 0387.53010
[9] S. Mizohata, The Theory of Partial Differential Equations, Cambridge University Press, Cambridge (1973). · Zbl 0263.35001
[10] S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).
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