# Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE

@inproceedings{The2010ConformalGO, title={Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE}, author={Dennis The}, year={2010} }

Of all real Lagrangian–Grassmannians LG(n, 2n), only LG(2, 4) admits a distinguished (Lorentzian) conformal structure and hence is identified with the indefinite Möbius space S. Using Cartan’s method of moving frames, we study hyperbolic (timelike) surfaces in LG(2, 4) modulo the conformal symplectic group CSp(4,R). This CSp(4,R)-invariant classification is also a contact-invariant classification of (in general, highly non-linear) second order scalar hyperbolic PDE in the plane. Via LG(2, 4… Expand

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