Titlebook: Symmetries and Overdetermined Systems of Partial Differential Equations; Michael Eastwood,Willard Miller Book 2008 Springer-Verlag New Yor

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Overdetermined Systems, Conformal Differential Geometry, and the BGG Complex equations”. The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined systems obtained recently in joint work with T.P. Branson, M.G. Eastwood, and A.R. Gover. First a simple special case is discussed, then the (Riemannian) procedure is d

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Generalized Wilczynski Invariants for Non-Linear Ordinary Differential Equationsinvariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship of such equations with deformation theory of rational curves on complex algebraic surfaces.

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Notes on Projective Differential GeometryThese notes aim to remedy this deficit and present several reasons why this should be done at this time. The deeper underlying reason is that projective differential geometry provides the most basic application of what has come to be known as the ‘Bernstein-Gelfand-Gelfand machinery’. As such, it is

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Fine Structure for Second Order Superintegrable Systemsendent constants of the motion polynomial in the momenta, the maximum possible. If the constants are all quadratic the system is second order superintegrable. Such systems have remarkable properties: multi-integrability and multi-separability, a quadratic algebra of symmetries whose representation t

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On Geometric Properties of Joint Invariants of Killing Tensorsf constant curvature under the action of the corresponding isometry group. We also discuss geometric properties of joint invariants of Killing two-tensors defined in the Euclidean plane to formulate and prove an analogue of the Weyl theorem on joint invariants. In addition, it is shown how the joint