Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry
نویسندگان
چکیده
منابع مشابه
Invariant Prolongation of Overdetermined PDEs in Projective, Conformal and Grassmannian Geometry
This is the second in a series of papers on natural modification of the normal tractor connection in a parabolic geometry, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in [5] and then compute the prolongation covariant derivatives for a number of interesting examples in projective, con...
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BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The expl...
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We investigate second order quasilinear equations of the form fijuxixj = 0, where u is a function of n independent variables x1, ..., xn, and the coefficients fij depend on the first order derivatives p = ux1 , ..., p n = uxn only. We demonstrate that the natural equivalence group of the problem is isomorphic to SL(n + 1, R), which acts by projective transformations on the space P with coordina...
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This is an expanded version of a series of two lectures given at the IMA summer program “Symmetries and Overdetermined Systems of Partial Differential Equations”. The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined system obtained recently in joint work with T.P. Branson, M.G. Eastwood, and A.R. Gover. First a simple special cas...
متن کاملOverdetermined systems, conformal differential geometry, and the BGG complex
This is an expanded version of a series of two lectures given at the IMA summer program “Symmetries and Overdetermined Systems of Partial Differential Equations”. The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined system obtained recently in joint work with T.P. Branson, M.G. Eastwood, and A.R. Gover. First a simple special cas...
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ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2011
ISSN: 0232-704X,1572-9060
DOI: 10.1007/s10455-011-9306-9