Representação Spinorial de subvariedade no espaço de de Sitter

Autores

  • Samuel A Wainer

DOI:

https://doi.org/10.5540/03.2023.010.01.0091

Palavras-chave:

Imersão, Spinores, Álgebras de Clifford, Espaço de de Sitter

Resumo

Desde o primeiro trabalho de Thomas Friedrich, mostrando que imersões isométricas de superfícies no espaço euclidiano estão relacionadas com spinores e a equação de Dirac, vários trabalhos surgiram generalizando essa abordagem para variedades Spin mais gerais; em particular o caso de imersões em espaços curvatura constante. No presente trabalho investigamos a caracterização spinorial de imersões isométricas de variedades Spin e SpinC no espaço de de Sitter.

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Biografia do Autor

Samuel A Wainer

ITA, São José dos Campos, SP

Referências

Pierre Bayard. “On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space”. Em: Journal of Geometry and Physics 74 (2013), pp. 289–313.

Pierre Bayard, Marie-Amélie Lawn e Julien Roth. “Spinorial representation of submanifolds in Riemannian space forms”. Em: Pacific Journal of Mathematics 291.1 (2017), pp. 51–80.

Pierre Bayard, Marie-Amélie Lawn e Julien Roth. “Spinorial representation of surfaces into 4-dimensional space forms”. Em: Annals of Global Analysis and Geometry 44 (2013), pp. 433–453.

Paul Adrian Maurice Dirac. “The electron wave equation in de-Sitter space”. Em: Annals of Mathematics (1935), pp. 657–669.

Rafael de Freitas Leão e Samuel Augusto Wainer. “Immersion in Rn by Complex Spinors”. Em: Advances in Applied Clifford Algebras 28.2 (2018), p. 44.

Thomas Friedrich. “On the spinor representation of surfaces in Euclidean 3-space”. Em: Journal of Geometry and Physics 28.1-2 (1998), pp. 143–157.

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Waldyr A Rodrigues e Samuel A Wainer. “Notes on conservation laws, equations of motion of matter, and particle fields in Lorentzian and teleparallel de sitter space-time structures”. Em: Advances in Mathematical Physics 2016 (2016).

Waldyr Alves Rodrigues e Samuel A Wainer. “On the Motion of a Free Particle in the de Sitter Manifold”. Em: Advances in Applied Clifford Algebras 27 (2017), pp. 1761–1767.

Samuel A Wainer. “Geodésicas e momento angular constante no espaço Anti-de Sitter (2,3)”. Em: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 8.1 (2021).

Samuel Augusto Wainer e Rafael de Freitas Leão. “Representação spinorial de variedades SpinC em formas espaciais”. Em: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 7.1 (2020).

A Waldyr Jr e Edmundo C de Oliveira. The Many Faces of Maxwell, Dirac and Einstein Equations: A Clifford Bundle Approach. Springer-Verlag GmbH., 2007.

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Publicado

2023-12-18

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