Invariant local twistor calculus for quaternionic structures and related geometries

Details Invariant local twistor calculus for quaternionic structures and related geometries Invariant local twistor calculus for quaternionic structures and related geometries

1998-05-05

arxiv.org/abs/math/9805016v1

Mathematics

Differential Geometry

44 pages

Scientific paper

10.1016/S0393-0440(99)00018-2

New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all invariants and invariant operators arise from these universal operators and that they may be used to reduce all invariants problems to corresponding algebraic problems involving homomorphisms between modules of certain parabolic subgroups of Lie groups. Explicit application of the operators is illustrated by the construction of all non-standard operators between exterior forms on a large class of the geometries which includes the quaternionic structures.

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