2012/10/27 by Boris Doubrov, Doubrov, Boris, Igor Zelenko +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #58A17 #58A30 #Algebraic Geometry and Number Theory #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1210.7334
openalex publication_date 2012/10/27 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
Motivated by the geometric theory of differential equations and the\nvariational approach to the equivalence problem for geometric structures on\nmanifolds, we consider the problem of equivalence for distributions with fixed\nsubmanifolds of flags on each fiber. We call them flag structures. The\nconstruction of the canonical frames for these structures can be given in the\ntwo prolongation steps: the first step, based on our previous works, gives the\ncanonical bundle of moving frames for the fixed submanifolds of flags on each\nfiber and the second step consists of the prolongation of the bundle obtained\nin the first step. The bundle obtained in the first step is not as a rule a\nprincipal bundle so that the classical Tanaka prolongation procedure for\nfiltered structures can not be applied to it. However, under natural\nassumptions on submanifolds of flags and on the ambient distribution, this\nbundle satisfies a nice weaker property. The main goal of the present paper is\nto formalize this property, introducing the so-called quasi-principle frame\nbundles, and to generalize the Tanaka prolongation procedure to these bundles.\nApplications to the equivalence problems for systems of differential equations\nof mixed order, bracket generating distributions, sub-Riemannian and more\ngeneral structures on distributions are given.\n