Projective structure, $\widetilde{\mathrm{SL}}(3,{\mathbb R})$ and the symplectic Dirac operator

Marie Holíková; Libor Křižka; Petr Somberg

Projective structure, $\widetilde{\mathrm{SL}}(3,{\mathbb R})$ and the symplectic Dirac operator

Differential Geometry 2016-04-18 v1 Mathematical Physics Analysis of PDEs math.MP Symplectic Geometry

Authors: Marie Holíková , Libor Křižka , Petr Somberg

Abstract

Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is $\widetilde{\mathrm{SL}}(3,{\mathbb R})$ .

Keywords

symplectic geometry dirac operators projective geometry

Cite

@article{arxiv.1604.04376,
  title  = {Projective structure, $\widetilde{\mathrm{SL}}(3,{\mathbb R})$ and the symplectic Dirac operator},
  author = {Marie Holíková and Libor Křižka and Petr Somberg},
  journal= {arXiv preprint arXiv:1604.04376},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1512.08203

Projective structure, $\widetilde{\mathrm{SL}}(3,{\mathbb R})$ and the symplectic Dirac operator

Abstract

Keywords

Cite

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