Geometrical wave equation and the cauchy-like theorem for octonions
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://www.ijpam.eu/contents/2012-79-3/6/6.pdf http://hdl.handle.net/11449/73658 |
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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Repositório Institucional da UNESP |
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Geometrical wave equation and the cauchy-like theorem for octonionsCauchy integralHypercomplexQuaternionsRiemann 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.UNESP - Sao Paulo State University S.J. Rio Preto Campus, 15054-000, S̃ao Jośe do Rio PretoDepartment of Mathematics UFMA - Federal University of Maranh̃ao, 65085-580, Maranh̃aoUNESP - Sao Paulo State University S.J. Rio Preto Campus, 15054-000, S̃ao Jośe do Rio PretoUniversidade Estadual Paulista (Unesp)Universidade Federal do Maranhão (UFMA)Borges Neto, Manoel Ferreira [UNESP]Marão, José Antônio Pires Ferreira2014-05-27T11:27:06Z2014-05-27T11:27:06Z2012-10-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article453-464application/pdfhttp://www.ijpam.eu/contents/2012-79-3/6/6.pdfInternational Journal of Pure and Applied Mathematics, v. 79, n. 3, p. 453-464, 2012.1311-8080http://hdl.handle.net/11449/736582-s2.0-848670757872-s2.0-84867075787.pdf7955413331293674Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Pure and Applied Mathematics0,139info:eu-repo/semantics/openAccess2023-12-09T06:23:06Zoai:repositorio.unesp.br:11449/73658Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:52:12.105702Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Geometrical wave equation and the cauchy-like theorem for octonions |
title |
Geometrical wave equation and the cauchy-like theorem for octonions |
spellingShingle |
Geometrical wave equation and the cauchy-like theorem for octonions Borges Neto, Manoel Ferreira [UNESP] Cauchy integral Hypercomplex Quaternions |
title_short |
Geometrical wave equation and the cauchy-like theorem for octonions |
title_full |
Geometrical wave equation and the cauchy-like theorem for octonions |
title_fullStr |
Geometrical wave equation and the cauchy-like theorem for octonions |
title_full_unstemmed |
Geometrical wave equation and the cauchy-like theorem for octonions |
title_sort |
Geometrical wave equation and the cauchy-like theorem for octonions |
author |
Borges Neto, Manoel Ferreira [UNESP] |
author_facet |
Borges Neto, Manoel Ferreira [UNESP] Marão, José Antônio Pires Ferreira |
author_role |
author |
author2 |
Marão, José Antônio Pires Ferreira |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Federal do Maranhão (UFMA) |
dc.contributor.author.fl_str_mv |
Borges Neto, Manoel Ferreira [UNESP] Marão, José Antônio Pires Ferreira |
dc.subject.por.fl_str_mv |
Cauchy integral Hypercomplex Quaternions |
topic |
Cauchy integral Hypercomplex Quaternions |
description |
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. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-10-09 2014-05-27T11:27:06Z 2014-05-27T11:27:06Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www.ijpam.eu/contents/2012-79-3/6/6.pdf International Journal of Pure and Applied Mathematics, v. 79, n. 3, p. 453-464, 2012. 1311-8080 http://hdl.handle.net/11449/73658 2-s2.0-84867075787 2-s2.0-84867075787.pdf 7955413331293674 |
url |
http://www.ijpam.eu/contents/2012-79-3/6/6.pdf http://hdl.handle.net/11449/73658 |
identifier_str_mv |
International Journal of Pure and Applied Mathematics, v. 79, n. 3, p. 453-464, 2012. 1311-8080 2-s2.0-84867075787 2-s2.0-84867075787.pdf 7955413331293674 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Pure and Applied Mathematics 0,139 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
453-464 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129132198887424 |