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

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Hamiltonian Curve Flows in lie Groups , ⊂ , and Vector Nls, mKdV, Sine-Gordon Soliton Equations.. ⊂., generalizing previous work on integrable curve flows in Riemannian symmetric spaces .. The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group .. This is shown to yield the two known .(. – l)-invariant vector generalizations of both the

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Geometry of Non-Regular Separationntains as special cases both fixed-energy separation and constrained separation of Helmholtz and Schödinger equations (not necessarily orthogonal). The geometrical approach to non-regular separation allows to explain why it is possible to find some coordinates in Euclidean 3-space where the R-separa

Functional

Higher Symmetries of the Square of the Laplacian Again, there is a close connection with conformal geometry. There are three main steps in our construction. The first is to show that the symbol of a symmetry is constrained by an overdetermined partial differential equation. The second is to show existence of symmetries with specified symbol (usin

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Metric Connections in Projective Differential Geometryrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. Thi

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Notes on Projective Differential Geometry(n,ℝ) (rather than SO(.) as one might naively expect). Projective differential geometry also provides the simplest setting in which overdetermined systems of partial differential equations naturally arise.

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On Geometric Properties of Joint Invariants of Killing Tensorssors 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 invariants manifest themselves in the theory of superintegrable Hamiltonian systems.