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Higher symmetries of the laplacian
We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues ofExpand
The Penrose Transform: Its Interaction with Representation Theory
Part 1 Lie algebras and flag manifolds: some structure theory borel and parabolic subalgebras generalized flag varieties fibrations of generalized flag varieties. Part 2 Homogeneous vector bundles onExpand
Cohomology and massless fields
The geometry of twistors was first introduced in Penrose [28]. Since that time it has played a significant role in solutions of various problems in mathemetical physics of both a linear and nonlinearExpand
Metric Connections in Projective Differential Geometry
We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positiveExpand
Complex Paraconformal Manifolds – their Differential Geometry and Twistor Theory
A complex paraconformal manifold is a/^-dimensional complex manifold (/?, q > 2) whose tangent bündle factors äs a tensor product of two bundles of ranks p and q. We also assume that we are given aExpand
Conformal circles and parametrizations of curves in conformal manifolds
We give a simple ODE for the conformal circles on a conformal manifold, which gives the curves together with a family of preferred parametrizations. These parametrizations endow each conformal circleExpand
PROLONGATIONS OF GEOMETRIC OVERDETERMINED SYSTEMS
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case ofExpand
ZERO-ENERGY FIELDS ON COMPLEX PROJECTIVE SPACE
We consider complex projective space with its Fubini–Study metric and the X-ray transform defined by integration over its geodesics. We identify the kernel of this transform acting on symmetricExpand
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