Variations on the de Rham Complex
Summary: Familiar identities with grad, div, and curl may be framed as the de Rham complex on an open set in Euclidean space. The corresponding complex on the three-sphere, when considered in a vector form, leads naturally to the Bernstein-Gelfand-Gelfand complex in representation theory.
- University of Adelaide Australia
projective differential geometry, conformal differential geometry, projective three-sphere, parabolic subgroup, Projective differential geometry, round sphere, Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), Bernstein-Gelfand-Gelfand complex, symmetry group, conformal three-sphere, Differential geometry of homogeneous manifolds, CR geometry, Contact manifolds (general theory), contact three-sphere, Conformal differential geometry, parabolic differential geometry, de Rham theory in global analysis
projective differential geometry, conformal differential geometry, projective three-sphere, parabolic subgroup, Projective differential geometry, round sphere, Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), Bernstein-Gelfand-Gelfand complex, symmetry group, conformal three-sphere, Differential geometry of homogeneous manifolds, CR geometry, Contact manifolds (general theory), contact three-sphere, Conformal differential geometry, parabolic differential geometry, de Rham theory in global analysis
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