Quaternion functions and four-dimensional Riemannian metrics

Detalhes bibliográficos
Autor(a) principal: Machado, J. M. [UNESP]
Data de Publicação: 2005
Outros Autores: Borges, M. F. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://hdl.handle.net/11449/224616
Resumo: In this paper we discuss homeomorphic transformations of Riemannian metrics in four-dimensional Riemannian manifolds, and show that these transformations are related to the solutions of Beltrami-type systems of differentiable, quaternionic functions. It is introduced the concept of quaternionic factorization of metrics, and demonstrated that monogenic functions are a particular case in a larger class of quaternionic differentiable functions. This class is formed by the solutions of an homogeneous operator equation, constructed for any factorizable, Riemannian metric. © Dynamic Publishers, Inc.
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spelling Quaternion functions and four-dimensional Riemannian metricsIn this paper we discuss homeomorphic transformations of Riemannian metrics in four-dimensional Riemannian manifolds, and show that these transformations are related to the solutions of Beltrami-type systems of differentiable, quaternionic functions. It is introduced the concept of quaternionic factorization of metrics, and demonstrated that monogenic functions are a particular case in a larger class of quaternionic differentiable functions. This class is formed by the solutions of an homogeneous operator equation, constructed for any factorizable, Riemannian metric. © Dynamic Publishers, Inc.UNESP - State University of São Paulo at São José do Rio Preto Department of Computing, 15054-000 - Sao Jose do Rio PretoUNESP - State University of São Paulo at São José do Rio Preto Department of Computing, 15054-000 - Sao Jose do Rio PretoUniversidade Estadual Paulista (UNESP)Machado, J. M. [UNESP]Borges, M. F. [UNESP]2022-04-28T20:01:33Z2022-04-28T20:01:33Z2005-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article15-31Communications in Applied Analysis, v. 9, n. 1, p. 15-31, 2005.1083-2564http://hdl.handle.net/11449/2246162-s2.0-25844472369Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications in Applied Analysisinfo:eu-repo/semantics/openAccess2022-04-28T20:01:33Zoai:repositorio.unesp.br:11449/224616Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:59:51.638990Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Quaternion functions and four-dimensional Riemannian metrics
title Quaternion functions and four-dimensional Riemannian metrics
spellingShingle Quaternion functions and four-dimensional Riemannian metrics
Machado, J. M. [UNESP]
title_short Quaternion functions and four-dimensional Riemannian metrics
title_full Quaternion functions and four-dimensional Riemannian metrics
title_fullStr Quaternion functions and four-dimensional Riemannian metrics
title_full_unstemmed Quaternion functions and four-dimensional Riemannian metrics
title_sort Quaternion functions and four-dimensional Riemannian metrics
author Machado, J. M. [UNESP]
author_facet Machado, J. M. [UNESP]
Borges, M. F. [UNESP]
author_role author
author2 Borges, M. F. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Machado, J. M. [UNESP]
Borges, M. F. [UNESP]
description In this paper we discuss homeomorphic transformations of Riemannian metrics in four-dimensional Riemannian manifolds, and show that these transformations are related to the solutions of Beltrami-type systems of differentiable, quaternionic functions. It is introduced the concept of quaternionic factorization of metrics, and demonstrated that monogenic functions are a particular case in a larger class of quaternionic differentiable functions. This class is formed by the solutions of an homogeneous operator equation, constructed for any factorizable, Riemannian metric. © Dynamic Publishers, Inc.
publishDate 2005
dc.date.none.fl_str_mv 2005-01-01
2022-04-28T20:01:33Z
2022-04-28T20:01:33Z
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 Communications in Applied Analysis, v. 9, n. 1, p. 15-31, 2005.
1083-2564
http://hdl.handle.net/11449/224616
2-s2.0-25844472369
identifier_str_mv Communications in Applied Analysis, v. 9, n. 1, p. 15-31, 2005.
1083-2564
2-s2.0-25844472369
url http://hdl.handle.net/11449/224616
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Communications in Applied Analysis
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 15-31
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_ 1808128590432174080

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