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Differential operators and immersions of a Riemann surface into a Grassmannian

✍ Scribed by Indranil Biswas

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
90 KB
Volume
41
Category
Article
ISSN
0393-0440

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✦ Synopsis

We consider equivariant holomorphic immersions of a universal cover X of a compact Riemann surface X into a Grassmannian G(n, C 2n ) satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to GL(2n, C) that takes the natural action of the Galois group on X to the action of the Galois group on G(n, C 2n ) defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism.

πŸ“œ SIMILAR VOLUMES

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✍ Ulrich Heise πŸ“‚ Article πŸ“… 1994 πŸ› Springer Netherlands 🌐 English βš– 820 KB

Fundamental solutions of the differential operators for the potential problem and the elastostatic problem are established. They are not defined on the ordinary three-dimensional space as the classical I/R solution and Kelvin's solution but on Riemann spaces with circular branch lines and a finite a