Geometrical wave equation and the cauchy-like theorem for octonions

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Data

2012-10-09

Autores

Borges Neto, Manoel Ferreira [UNESP]
Marão, José Antônio Pires Ferreira

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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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Palavras-chave

Cauchy integral, Hypercomplex, Quaternions

Como citar

International Journal of Pure and Applied Mathematics, v. 79, n. 3, p. 453-464, 2012.