References
G. A. Banaru, “Connections adjoint to the equation y 5 = f(x, y, y′, y″, y (3) , y (4)),” Deposited at VINITI, No. 3948–V90.
G. A. Banaru, “Projective connection adjoint to an ordinary fifth-order differential equation,” Deposited at VINITI, No. 847–V92.
E. Cartan, “La geometria de las ecuaciones diferenciales de terces orden,” Rev. Mat. Hisp. Amer., Ser. 4a, 1, 3–33 (1941).
V. Glizburg, “On the fundamental group G p−1 n of connection generated by the differential system of higher order,” In: Acta Comment. Univ. Tartuensis, III Sugiskoolist (Topol. Rakendused Algebras Different. Geometeetrias), 19–22 Sept. 1991, Tartu (1992), pp. 41–46.
V. Glizburg, “Fibre bundle with fundamentall-group connection associated with ordinary differential system of high order,” In: Webs and Quasigroups [in Russian], Tver’ (1992), pp. 42–49.
V. I. Glizburg, “Fundamental group and curvature object of Cartan connection torsion that is invariantly defined by an ordinary differential system of order p˙ > 3,” Deposited at VINITI, No. 4290–V91.
V. I. Glizburg, “Reduction of a p-frame bundle invariantly defined by an ordinary differential system of order p˙ > 3,” Deposited at VINITI, No. 4291–V91.
V. I, Glizburg, “An invariant description of an ordinary higher-order differential system,” Izv. Vuzov, Mat., No. 1, 51–57 (1992).
L. E. Evtushik, “Nonlinear higher-order connections,” Izv. Vuzov, Mat., No. 2, 32–44 (1969).
L. E. Evtushik, “Reductive Cartan connections and generalized affinely normalized Norden structures,” Izv. Vuzov, Mat.. No. 5, 87–96 (1974).
L. E. Evtushik, “Basis differential operator over p-velocity space and its geometric applications,” In: Theoretical and Applied Problems in Mathematics, III. Abstracts of Reports [in Russian], Tartu (1985), pp. 28–33.
L. E. Evtushik, “Stable nonlinear higher-order connections and reduction to them of ordinary differential systems of the corresponding order,” In: Function Theory and Its Application [in Russian], Kemerovo (1985), pp. 48–56.
L. E. Evtushik, “Fundamental studies in geometry of systems of higher-order ordinary differential equations in the Laptev–Vasil’ev school,” In: International Scientific School “Lobachevskii and Modern Geometry,” Kazan’, August 18–22, 1992. Abstracts of Reports, Pt. 1 [in Russian], Kazan’ (1992), pp. 30-31.
L. E. Evtushik and V. B. Tret’yakov, “On structures defined by a system of higher-order ordinary differential equations,” In: Proceedings of a Geometric Workshop [in Russian], 6, All-Union Institute for Scientific and Technical Information, Moscow (1974), pp. 243–256.
L. E. Evtushik and V. B. Tret’yakov, “Invariant description of ordinary systems in terms of nonlinear connections,” Izv. Vuzov, Mat., No. 1, 21–32 (1986).
L. E. Evtushik, Yu. G. Lumiste, N. M. Ostianu, and A. P. Shirokov, “Differential-geometric structures on manifolds,” In: Progress in Science and Techology, Series on Problems in Geometry [in Russian], 9, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1984), pp. 1–246.
G. F. Laptev, “Differential geometry of immersed manifolds. A group-theoretic method of differential-geometric studies,” Trudy Mosk. Mat. Obshch., 2, 275–382 (1952).
G. F. Laptev, “Geometry of differential equations,” In: 1st All-Union Geometric Conference, Abstracts of Reports [in Russian], Kiev (1962), pp. 6–7.
I. Dzh. Meboniya, “Reduction of strongly reducible fifth-order differential systems to the stable nonlinear connection structure,” In: Diferential Geometry of Figure Manifolds [in Russian], No. 21, Kaliningrad University, Kaliningrad (1990), pp. 61–65.
I. Dzh. Meboniya, “Structure of linear connection for a sixth-order differential system,” Deposited at Gruz. NIINTI, No. 773–C92
V. I. Pan’zhenskii, “Motions in Kawaguchi spaces with special metrics,” Izv. Vuzov, Mat., No. 12, 77–82 (2007).
N. V. Stepanov, “Differential-geometric theory of the equation y (n) = f(x, y, y′,…, y (n−1)),” In: Progress in Science and Technology, Series on Problems in Geometry [in Russian], 8, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1977), pp. 47–66.
N. V. Stepanov, “Geometry of differential equations,” In: Progress in Science and Technology, Series on Problems in Geometry [in Russian], 12, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1981), pp. 127–164.
A. M. Vasil’ev, “Invariant analytical methods in differential geometry,” Dokl. Akad. Nauk SSSR, 79, No. 1, 5–7 (1951).
A. M. Vasil’ev, Theory of Differential-Geometric Structures [in Russian], MGU, Moscow (1987).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 123, Geometry, 2009.
Rights and permissions
About this article
Cite this article
Evtushik, L.E. German Fedorovich Laptev, his unique method, achievements, and modern contribution. On the 100th anniversary of the birth of our teacher. J Math Sci 169, 249–281 (2010). https://doi.org/10.1007/s10958-010-0048-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-0048-1