Representação Spinorial de subvariedade no espaço de de Sitter
DOI:
https://doi.org/10.5540/03.2023.010.01.0091Keywords:
Imersão, Spinores, Álgebras de Clifford, Espaço de de SitterAbstract
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.
Downloads
References
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.
Feza Gursey. “Introduction to group theory”. Em: Les Houches Summer Shcool of Theoretical Physics: Relativity, Groups and Topology. 1964, pp. 91–164.
Marie-Amélie Lawn. “Immersions of Lorentzian surfaces in R2,1”. Em: Journal of Geometry and Physics 58.6 (2008), pp. 683–700.
Marie-Amélie Lawn e Julien Roth. “Spinorial characterizations of surfaces into 3-dimensional pseudo-Riemannian space forms”. Em: Mathematical Physics, Analysis and Geometry 14 (2011), pp. 185–195.
Bertrand Morel. “Surfaces in S3 and H3 via spinors”. Em: Séminaire de théorie spectrale et géométrie 23 (2005), pp. 131–144.
JG Pereira e AC Sampson. “de Sitter geodesics: reappraising the notion of motion”. Em: General Relativity and Gravitation 44 (2012), pp. 1299–1308.
JG Pereira, AC Sampson e LL Savi. “de Sitter transitivity, conformal transformations and conservation laws”. Em: International Journal of Modern Physics D 23.04 (2014), p. 1450035.
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.
