Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups
ABSTRACT: We give a classification of flat affine left invariant metric geometric structures on simply connected Lie groups of dimensions two and three. We give some examples of non flat metrics in dimensions up to four.
- Autores:
-
Buitrago Vélez, Juan Felipe
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2021
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/21478
- Acceso en línea:
- http://hdl.handle.net/10495/21478
- Palabra clave:
- Metric spaces
Lie groups
Lie algebras
Riemannian manifolds
Varieties (Universal algebra)
Invariants
Affine algebraic groups
Geometry, Riemannian
Distance geometry
Variedades (Álgebra universal)
http://id.loc.gov/authorities/subjects/sh85084441
http://id.loc.gov/authorities/subjects/sh85076786
http://id.loc.gov/authorities/subjects/sh85076782
http://id.loc.gov/authorities/subjects/sh85114045
http://id.loc.gov/authorities/subjects/sh87001104
http://id.loc.gov/authorities/subjects/sh85067665
http://id.loc.gov/authorities/subjects/sh96011312
http://id.loc.gov/authorities/subjects/sh85054159
http://id.loc.gov/authorities/subjects/sh85038508
- Rights
- openAccess
- License
- Atribución-NoComercial-CompartirIgual 2.5 Colombia (CC BY-NC-SA 2.5 CO)
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|
| dc.title.spa.fl_str_mv |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| title |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| spellingShingle |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups Metric spaces Lie groups Lie algebras Riemannian manifolds Varieties (Universal algebra) Invariants Affine algebraic groups Geometry, Riemannian Distance geometry Variedades (Álgebra universal) http://id.loc.gov/authorities/subjects/sh85084441 http://id.loc.gov/authorities/subjects/sh85076786 http://id.loc.gov/authorities/subjects/sh85076782 http://id.loc.gov/authorities/subjects/sh85114045 http://id.loc.gov/authorities/subjects/sh87001104 http://id.loc.gov/authorities/subjects/sh85067665 http://id.loc.gov/authorities/subjects/sh96011312 http://id.loc.gov/authorities/subjects/sh85054159 http://id.loc.gov/authorities/subjects/sh85038508 |
| title_short |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| title_full |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| title_fullStr |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| title_full_unstemmed |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| title_sort |
Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groups |
| dc.creator.fl_str_mv |
Buitrago Vélez, Juan Felipe |
| dc.contributor.advisor.none.fl_str_mv |
Saldarriaga Ortiz, Omar Darío |
| dc.contributor.author.none.fl_str_mv |
Buitrago Vélez, Juan Felipe |
| dc.subject.lcsh.none.fl_str_mv |
Metric spaces Lie groups Lie algebras Riemannian manifolds Varieties (Universal algebra) Invariants Affine algebraic groups Geometry, Riemannian Distance geometry |
| topic |
Metric spaces Lie groups Lie algebras Riemannian manifolds Varieties (Universal algebra) Invariants Affine algebraic groups Geometry, Riemannian Distance geometry Variedades (Álgebra universal) http://id.loc.gov/authorities/subjects/sh85084441 http://id.loc.gov/authorities/subjects/sh85076786 http://id.loc.gov/authorities/subjects/sh85076782 http://id.loc.gov/authorities/subjects/sh85114045 http://id.loc.gov/authorities/subjects/sh87001104 http://id.loc.gov/authorities/subjects/sh85067665 http://id.loc.gov/authorities/subjects/sh96011312 http://id.loc.gov/authorities/subjects/sh85054159 http://id.loc.gov/authorities/subjects/sh85038508 |
| dc.subject.lemb.none.fl_str_mv |
Variedades (Álgebra universal) |
| dc.subject.lcshuri.none.fl_str_mv |
http://id.loc.gov/authorities/subjects/sh85084441 http://id.loc.gov/authorities/subjects/sh85076786 http://id.loc.gov/authorities/subjects/sh85076782 http://id.loc.gov/authorities/subjects/sh85114045 http://id.loc.gov/authorities/subjects/sh87001104 http://id.loc.gov/authorities/subjects/sh85067665 http://id.loc.gov/authorities/subjects/sh96011312 http://id.loc.gov/authorities/subjects/sh85054159 http://id.loc.gov/authorities/subjects/sh85038508 |
| description |
ABSTRACT: We give a classification of flat affine left invariant metric geometric structures on simply connected Lie groups of dimensions two and three. We give some examples of non flat metrics in dimensions up to four. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-08-03T15:21:09Z |
| dc.date.available.none.fl_str_mv |
2021-08-03T15:21:09Z |
| dc.date.issued.none.fl_str_mv |
2021 |
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info:eu-repo/semantics/bachelorThesis |
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http://purl.org/coar/version/c_b1a7d7d4d402bcce |
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info:eu-repo/semantics/draft |
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http://purl.org/coar/resource_type/c_7a1f |
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https://purl.org/redcol/resource_type/TP |
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Tesis/Trabajo de grado - Monografía - Pregrado |
| format |
http://purl.org/coar/resource_type/c_7a1f |
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draft |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10495/21478 |
| url |
http://hdl.handle.net/10495/21478 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.rights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
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Atribución-NoComercial-CompartirIgual 2.5 Colombia (CC BY-NC-SA 2.5 CO) |
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http://creativecommons.org/licenses/by-nc-sa/2.5/co/ |
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openAccess |
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Medellín, Colombia |
| institution |
Universidad de Antioquia |
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andres.perez@udea.edu.co |
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1805390204388769792 |
| spelling |
Saldarriaga Ortiz, Omar DaríoBuitrago Vélez, Juan Felipe2021-08-03T15:21:09Z2021-08-03T15:21:09Z2021http://hdl.handle.net/10495/21478ABSTRACT: We give a classification of flat affine left invariant metric geometric structures on simply connected Lie groups of dimensions two and three. We give some examples of non flat metrics in dimensions up to four.11application/pdfenginfo:eu-repo/semantics/draftinfo:eu-repo/semantics/bachelorThesishttp://purl.org/coar/resource_type/c_7a1fhttps://purl.org/redcol/resource_type/TPTesis/Trabajo de grado - Monografía - Pregradohttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/openAccessAtribución-NoComercial-CompartirIgual 2.5 Colombia (CC BY-NC-SA 2.5 CO)http://creativecommons.org/licenses/by-nc-sa/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-sa/4.0/Metric spacesLie groupsLie algebrasRiemannian manifoldsVarieties (Universal algebra)InvariantsAffine algebraic groupsGeometry, RiemannianDistance geometryVariedades (Álgebra universal)http://id.loc.gov/authorities/subjects/sh85084441http://id.loc.gov/authorities/subjects/sh85076786http://id.loc.gov/authorities/subjects/sh85076782http://id.loc.gov/authorities/subjects/sh85114045http://id.loc.gov/authorities/subjects/sh87001104http://id.loc.gov/authorities/subjects/sh85067665http://id.loc.gov/authorities/subjects/sh96011312http://id.loc.gov/authorities/subjects/sh85054159http://id.loc.gov/authorities/subjects/sh85038508Left invariant Lorentzian, hyperbolic and Riemannian metrics on Lie groupsMedellín, ColombiaMatemáticoPregradoFacultad de Ciencias Exactas y Naturales. Carrera de MatemáticasUniversidad de AntioquiaORIGINALBuitragoJuan_2021_MetricsLieGroups.pdfBuitragoJuan_2021_MetricsLieGroups.pdfTrabajo de grado de pregradoapplication/pdf282618http://bibliotecadigital.udea.edu.co/bitstream/10495/21478/1/BuitragoJuan_2021_MetricsLieGroups.pdf79a9cf694bcf99920dd0188681fa7eefMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81051http://bibliotecadigital.udea.edu.co/bitstream/10495/21478/2/license_rdfe2060682c9c70d4d30c83c51448f4eedMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/21478/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/21478oai:bibliotecadigital.udea.edu.co:10495/214782022-04-06 12:48:51.59Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.coTk9URTogUExBQ0UgWU9VUiBPV04gTElDRU5TRSBIRVJFClRoaXMgc2FtcGxlIGxpY2Vuc2UgaXMgcHJvdmlkZWQgZm9yIGluZm9ybWF0aW9uYWwgcHVycG9zZXMgb25seS4KCk5PTi1FWENMVVNJVkUgRElTVFJJQlVUSU9OIExJQ0VOU0UKCkJ5IHNpZ25pbmcgYW5kIHN1Ym1pdHRpbmcgdGhpcyBsaWNlbnNlLCB5b3UgKHRoZSBhdXRob3Iocykgb3IgY29weXJpZ2h0Cm93bmVyKSBncmFudHMgdG8gRFNwYWNlIFVuaXZlcnNpdHkgKERTVSkgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgdG8gcmVwcm9kdWNlLAp0cmFuc2xhdGUgKGFzIGRlZmluZWQgYmVsb3cpLCBhbmQvb3IgZGlzdHJpYnV0ZSB5b3VyIHN1Ym1pc3Npb24gKGluY2x1ZGluZwp0aGUgYWJzdHJhY3QpIHdvcmxkd2lkZSBpbiBwcmludCBhbmQgZWxlY3Ryb25pYyBmb3JtYXQgYW5kIGluIGFueSBtZWRpdW0sCmluY2x1ZGluZyBidXQgbm90IGxpbWl0ZWQgdG8gYXVkaW8gb3IgdmlkZW8uCgpZb3UgYWdyZWUgdGhhdCBEU1UgbWF5LCB3aXRob3V0IGNoYW5naW5nIHRoZSBjb250ZW50LCB0cmFuc2xhdGUgdGhlCnN1Ym1pc3Npb24gdG8gYW55IG1lZGl1bSBvciBmb3JtYXQgZm9yIHRoZSBwdXJwb3NlIG9mIHByZXNlcnZhdGlvbi4KCllvdSBhbHNvIGFncmVlIHRoYXQgRFNVIG1heSBrZWVwIG1vcmUgdGhhbiBvbmUgY29weSBvZiB0aGlzIHN1Ym1pc3Npb24gZm9yCnB1cnBvc2VzIG9mIHNlY3VyaXR5LCBiYWNrLXVwIGFuZCBwcmVzZXJ2YXRpb24uCgpZb3UgcmVwcmVzZW50IHRoYXQgdGhlIHN1Ym1pc3Npb24gaXMgeW91ciBvcmlnaW5hbCB3b3JrLCBhbmQgdGhhdCB5b3UgaGF2ZQp0aGUgcmlnaHQgdG8gZ3JhbnQgdGhlIHJpZ2h0cyBjb250YWluZWQgaW4gdGhpcyBsaWNlbnNlLiBZb3UgYWxzbyByZXByZXNlbnQKdGhhdCB5b3VyIHN1Ym1pc3Npb24gZG9lcyBub3QsIHRvIHRoZSBiZXN0IG9mIHlvdXIga25vd2xlZGdlLCBpbmZyaW5nZSB1cG9uCmFueW9uZSdzIGNvcHlyaWdodC4KCklmIHRoZSBzdWJtaXNzaW9uIGNvbnRhaW5zIG1hdGVyaWFsIGZvciB3aGljaCB5b3UgZG8gbm90IGhvbGQgY29weXJpZ2h0LAp5b3UgcmVwcmVzZW50IHRoYXQgeW91IGhhdmUgb2J0YWluZWQgdGhlIHVucmVzdHJpY3RlZCBwZXJtaXNzaW9uIG9mIHRoZQpjb3B5cmlnaHQgb3duZXIgdG8gZ3JhbnQgRFNVIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdApzdWNoIHRoaXJkLXBhcnR5IG93bmVkIG1hdGVyaWFsIGlzIGNsZWFybHkgaWRlbnRpZmllZCBhbmQgYWNrbm93bGVkZ2VkCndpdGhpbiB0aGUgdGV4dCBvciBjb250ZW50IG9mIHRoZSBzdWJtaXNzaW9uLgoKSUYgVEhFIFNVQk1JU1NJT04gSVMgQkFTRUQgVVBPTiBXT1JLIFRIQVQgSEFTIEJFRU4gU1BPTlNPUkVEIE9SIFNVUFBPUlRFRApCWSBBTiBBR0VOQ1kgT1IgT1JHQU5JWkFUSU9OIE9USEVSIFRIQU4gRFNVLCBZT1UgUkVQUkVTRU5UIFRIQVQgWU9VIEhBVkUKRlVMRklMTEVEIEFOWSBSSUdIVCBPRiBSRVZJRVcgT1IgT1RIRVIgT0JMSUdBVElPTlMgUkVRVUlSRUQgQlkgU1VDSApDT05UUkFDVCBPUiBBR1JFRU1FTlQuCgpEU1Ugd2lsbCBjbGVhcmx5IGlkZW50aWZ5IHlvdXIgbmFtZShzKSBhcyB0aGUgYXV0aG9yKHMpIG9yIG93bmVyKHMpIG9mIHRoZQpzdWJtaXNzaW9uLCBhbmQgd2lsbCBub3QgbWFrZSBhbnkgYWx0ZXJhdGlvbiwgb3RoZXIgdGhhbiBhcyBhbGxvd2VkIGJ5IHRoaXMKbGljZW5zZSwgdG8geW91ciBzdWJtaXNzaW9uLgo= |