Geometrical wave equation and the cauchy-like theorem for octonions
Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2012 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositório: | Repositório Institucional da UNESP |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unesp.br:11449/73658 |
| Acesso em linha: | http://www.ijpam.eu/contents/2012-79-3/6/6.pdf http://hdl.handle.net/11449/73658 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Cauchy integral Hypercomplex Quaternions |
| Resumo: | Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case. |
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