r-Tuple almost product structures

被引:0
作者
Kushner A.G. [1 ]
机构
[1] Astrakhan State University, Institute of Control Sciences of RAS, Astrakhan
基金
俄罗斯基础研究基金会;
关键词
Product Structure; Smooth Manifold; Jacobi Equation; Homogeneous Element; Negative Component;
D O I
10.1007/s10958-011-0482-8
中图分类号
学科分类号
摘要
A generalization of an almost product structure and an almost complex structure on smooth manifolds is constructed. The set of tensor differential invariants of type (2, 1) and the set of differential 2-forms for such structures are constructed. We show how these tensor invariants can be used to solve the classification problem for Monge-Ampère equations and Jacobi equations. © 2011 Springer Science+Business Media, Inc.
引用
收藏
页码:569 / 578
页数:9
相关论文
共 12 条
  • [1] Cotton E., Sur les invariants différentiels de quelques équations linearies aux dérivées partielles du second ordre, Ann. Sci. École Norm. Sup., 17, pp. 211-244, (1900)
  • [2] Kushner A.G., Almost product structures and Monge-Ampère equations, Lobachevskii J. Math., 23, pp. 151-181, (2006)
  • [3] Kushner A.G., A contact linearization problem for Monge-Ampère equations and Laplace invariants, Acta Appl. Math., 101, 1-3, pp. 177-189, (2008)
  • [4] Kushner A.G., Contact linearization of nondegenerate Monge-Ampère equations, Russ. Math., 52, 4, pp. 38-52, (2008)
  • [5] Kushner A.G., Classification of Monge-Ampère equations, Differential Equations: Geometry, Symmetries and Integrability. The Abel Symposium 2008. Proc. Of the Fifth Abel Symposium on Differential Equations: Geometry, Symmetries and Integrability, June 18-21, 2008, Tromsø, Norway, pp. 223-256, (2009)
  • [6] Kushner A.G., On contact equivalence of Monge-Ampère equations to linear equations with constant coefficients, Acta Appl. Math., 109, 1, pp. 197-210, (2010)
  • [7] Kushner A.G., Lychagin V.V., Rubtsov V.N., Contact Geometry and Nonlinear Differential Equations, 101, (2007)
  • [8] Laplace P.S., Recherches sur le calcul intégrals aux différences partielles, Mémoires de l'Académie royale des Sciences de Paris (1773)
  • [9] Oeuvres complètes, 9, (1966)
  • [10] Lie S., Über einige partielle Differential-Gleichungen zweiter Orduung, Math. Ann., 5, pp. 209-256, (1872)