Literature Cited
I. M. Gel'fand, S. G. Gindikin, and Z. Ya. Shapiro, "A local problem of integral geometry in a space of curves," Funkts. Anal. Prilozhen.,13, No. 2, 11–31 (1979).
I. M. Gel'fand and M. I. Graev, "Admissible n-dimensional complexes of curves in Cn," Funkts. Anal. Prilozhen.,14, No. 4, 36–44 (1980).
J. N. Bernstein and S. G. Gindikin, "Admissible families of curves," Seminar on Supermanifolds, Preprint, No. 3, Stockholm University (1986).
J. N. Bernstein and S. G. Gindikin, "Geometrical structure of admissible families of curves," Seminar on Supermanifolds, Preprint, No. 3, Stockholm University (1986).
J. N. Bernstein, "Description of admissible families of curves by critical points," Seminar on Supermanifolds, Preprint, No. 11, Stockholm University (1986).
S. G. Gindikin, "Integral geometry and twistors," Lect. Notes Math.,970, 2–42 (1982).
S. G. Gindikin, "Reduction of manifolds of rational curves and related problems of the theory of differential equations," Funkts. Anal. Prilozhen.,18, No. 4, 14–39 (1984).
I. M. Gel'fand and M. I. Graev, "Admissible complexes of lines in CPn," Funkts. Anal. Prilozhen.,2, No. 3, 39–52 (1968).
S. Lie, "Über Complex, insbesondere Linien and Kugel-Complex, mit Anwendung auf die Theorie partieller Differentialgleichungen I Ordnung," Math. Ann.,5, 145–256.
V. A. Ginzburg, "Symplectic geometry and the theory of representation," Funkts. Anal. Prilozhen.,17, No. 3, 75–76 (1983).
A. B. Goncharov, "Integral geometry on surfaces in the space," J. Geom. Physics (1989).
V. Guillemin and S. Sternberg, "Some problems in integral geometry and some related problems in microlocal analysis," Am. J. Math.,101, No. 4, 915–955 (1979).
V. Guillemin and S. Sternberg, Geometric Asymptotics [Russian translation], Mir, Moscow (1981).
I. M. Gel'fand and S. G. Gindikin, "Nonlocal inversion formulas in real integral geometry," Funkts. Anal. Prilozhen.,11, No. 3, 12–19 (1977).
E. T. Quinto, "Topological restrictions on double fibrations and Radon transforms," Proc. Am. Math. Soc.,101, No. 4.
K. Maius, "Linear complexes of k-planes," Funkts. Anal. Prilozhen.,19, No. 1, 79–80 (1984).
I. M. Gel'fand and S. Graev, and Z. Ya. Shapiro, "Integral geometry on k-dimensional planes," Funkts. Anal. Prilozhen.,1, No. 1, 17–31 (1967).
I. M. Gel'fand, S. G. Gindikin, and M. I. Graev, "Integral geometry in affine and projective spaces," Itogi Matem. Tekh., Seriya Sovremennye Problemy Matematiki,16, 53–226 (1980).
I. M. Gel'fand and G. S. Shmelev, "Geometric structures of double bundles and their relation to some problems of integral geometry," Funkts. Anal. Prilozhen.,17, No. 2, 7–22 (1983).
I. M. Gel'fand and A. B. Goncharov, "A characteriztion of Grassman manifolds," Dokl. Akad. Nauk SSSR,289, No. 5, 1031–1034 (1986).
A. B. Goncharov, "Admissible families of k-dimensional submanifolds,"300, No. 3, 535–539 (1988).
A. Tresse, "Sur les invariants differentielles des groupes continus des transformations," Acta Mat.,18, 1–88 (1894).
E. Cartan, "Sur les variétés à connexion projectif," in: Oeuvres, III,1, No. 70, Paris, pp. 825–862.
V. I. Arnol'd, Supplementary Chapters of the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1979).
P. Griffiths and J. Harris, Principles of Algebraic Geometry [Russian translation], Vol. 2, Mir, Moscow (1982).
A. B. Goncharov, "Integral geometry and contact transformations," (to appear).
M. Okonek, M. Schneider, and M. Spindler, Vector Bundles over Projective Spaces [Russian translation], Mir, Moscow (1985).
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Scientific Council of the Academy of Sciences of the USSR on the Complex Problem of "Cybernetics." Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 3, pp. 11–23, July–September, 1989.
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Goncharov, A.B. Integral geometry on families of k-dimensional submanifolds. Funct Anal Its Appl 23, 178–189 (1989). https://doi.org/10.1007/BF01079523
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DOI: https://doi.org/10.1007/BF01079523