On geometry of curves of flags of constant type
Tóm tắt
Từ khóa
Tài liệu tham khảo
Agrachev A.A., Feedback-invariant optimal control theory and differential geometry II. Jacobi curves for singular extremals, J. Dynam. Control Systems, 1998, 4(4), 583–604
Agrachev A.A., Gamkrelidze R.V., Feedback-invariant optimal control theory and differential geometry I. Regular extremals, J. Dynam. Control Systems, 1997, 3(3), 343–389
Agrachev A., Zelenko I., Principle invariants of Jacobi curves, In: Nonlinear Control in the Year 2000, 1, Lecture Notes in Control and Inform. Sci., 258, Springer, 2000, 9–21
Agrachev A., Zelenko I., Geometry of Jacobi curves. I, J. Dynam. Control Systems, 2002, 8(1), 93–140
Agrachev A., Zelenko I., Geometry of Jacobi curves. II, J. Dynam. Control Systems, 2002, 8(2), 167–215
Cartan E., La théorie des groupes finis et continus et la géométrie différentielle traitées par la méthode du repere mobile, Cahiers Scientifiques, 18, Gauthier-Villars, Paris, 1937
Derksen H., Weyman J., Quiver representations, Notices Amer. Math. Soc., 2005, 52(2), 200–206
Doubrov B., Projective reparametrization of homogeneous curves, Arch. Math. (Brno), 2005, 41(1), 129–133
Doubrov B., Generalized Wilczynski invariants for non-linear ordinary differential equations, In: Symmetries and Overdetermined Systems of Partial Differetial Equations, IMA Vol. Math. Appl., 144, Springer, New York, 2008, 25–40
Doubrov B.M., Komrakov B.P., Classification of homogeneous submanifolds in homogeneous spaces, Lobachevskii J. Math., 1999, 3, 19–38
Doubrov B., Machida Y., Morimoto T., Linear equations on filtered manifolds and submanifolds of flag varieties (manuscript)
Doubrov B., Zelenko I., A canonical frame for nonholonomic rank two distributions of maximal class, C. R. Acad. Sci. Paris, 2006, 342(8), 589–594
Doubrov B., Zelenko I., On local geometry of non-holonomic rank 2 distributions, J. Lond. Math. Soc., 2009, 80(3), 545–566
Doubrov B., Zelenko I., On local geometry of rank 3 distributions with 6-dimensional square, preprint available at http://arxiv.org/abs/0807.3267
Doubrov B., Zelenko I., Geometry of curves in parabolic homogeneous spaces, preprint available at http://arxiv.org/abs/1110.0226
Eastwood M., Slovák J., Preferred parameterisations on homogeneous curves, Comment. Math. Univ. Carolin., 2004, 45(4), 597–606
Fels M., Olver P.J., Moving coframes: I. A practical algorithm, Acta Appl. Math., 1998, 51(2), 161–213
Fels M., Olver P.J., Moving coframes: II. Regularization and theoretical foundations, Acta Appl. Math., 1999, 55(2), 127–208
Fulton W., Harris J., Representation Theory, Grad. Texts in Math., 129, Springer, New York, 1991
Gel’fand I.M., Lectrures on Linear Algebra, Interscience Tracts in Pure and Applied Mathematics, 9, Interscience, New York-London, 1961
Green M.L., The moving frame, differential invariants and rigidity theorem for curves in homogeneous spaces, Duke Math. J., 1978, 45(4), 735–779
Griffiths P., On Cartan’s method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry, Duke Math. J., 1974 41, 775–814
Humphreys J.E., Introduction to Lie Algebras and Representation Theory, 3rd printing, Grad. Texts in Math., 9, Springer, New York-Berlin, 1980
Jacobson N., Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, 10, Interscience, New York-London, 1962
Lie S., Theory der Transformationgruppen, 3, Teubner, Leipzig, 1893
Marí Beffa G., Poisson brackets associated to the conformal geometry of curves, Trans. Amer. Math. Soc., 2005, 357(7), 2799–2827
Marí Beffa G., On completely integrable geometric evolutions of curves of Lagrangian planes, Proc. Roy. Soc. Edinburgh Sect. A, Math., 2007, 137(1), 111–131
Marí Beffa G., Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds, Ann. Inst. Fourier (Grenoble), 2008, 58(4), 1295–1335
Marí Beffa G., Moving frames, geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors, Ann. Inst. Fourier (Grenoble) (in press)
Ovsienko V., Lagrange Schwarzian derivative and symplectic Sturm theory, Ann. Fac. Sci. Toulouse Math., 1993, 2(1), 73–96
Se-ashi Y., On differential invariants of integrable finite type linear differential equations, Hokkaido Math. J., 1988, 17(2), 151–195
Se-ashi Y., A geometric construction of Laguerre-Forsyth’s canonical forms of linear ordinary differential equations, In: Progress in Differential Geometry, Adv. Stud. Pure Math., 22, Kinokuniya, Tokyo, 1993, 265–297
Tanaka N., On differential systems, graded Lie algebras and pseudogroups, J. Math. Kyoto. Univ., 1970, 10, 1–82
Tanaka N., On the equivalence problems associated with simple graded Lie algebras, Hokkaido Math. J., 1979, 6(1), 23–84
Vinberg È.B., The Weyl group of a graded Lie algebra, Izv. Akad. Nauk SSSR Ser. Mat., 1976, 40(3), 488–526 (in Russian)
Vinberg È.B., Classification of homogeneous nilpotent elements of a semisimple graded Lie algebra, Trudy Sem. Vektor. Tenzor. Anal., 1979, 19, 155–177 (in Russian)
Wilczynski E.J., Projective Differential Geometry of Curves and Ruled Surfaces, Teubner, Leipzig, 1906
Zelenko I., Complete systems of invariants for rank 1 curves in Lagrange Grassmannians, In: Differential Geometry and its Applications, Prague, August 30–September 3, 2004, Matfyzpress, Prague, 2005, 367–382
Zelenko I., Li C., Parametrized curves in Lagrange Grassmannians, C. R. Math. Acad. Sci. Paris, 2007, 345(11), 647–652
Zelenko I., Li C., Differential geometry of curves in Lagrange Grassmannians with given Young diagram, Differential Geom. Appl., 2009, 27(6), 723–742
Sophus Lie’s 1880 Transformation Group Paper, Lie Groups: Hist., Frontiers and Appl., 1, Math Sci Press, Brookline, 1975