The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
- Autores
- Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás
- Año de publicación
- 2024
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.
Fil: Cardoso, Isolda Eugenia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Cosgaya, Ana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina - Materia
-
CHARACTERISTICALLY SOLVABLE LIE ALGEBRA
NILMANIFOLD
LEFT-INVARIANT METRIC
INDEX OF SYMMETRY
DISTRIBUTION OF SYMMETRY - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/239698
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CONICET Digital (CONICET) |
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The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifoldsCardoso, Isolda EugeniaCosgaya, AnaReggiani, Silvio NicolásCHARACTERISTICALLY SOLVABLE LIE ALGEBRANILMANIFOLDLEFT-INVARIANT METRICINDEX OF SYMMETRYDISTRIBUTION OF SYMMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.Fil: Cardoso, Isolda Eugenia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Cosgaya, Ana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Reggiani, Silvio Nicolás. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaCornell University2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/239698Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás; The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds; Cornell University; ArXiv.org; 2024; 5-2024; 1-242331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2404.19177info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2404.19177info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:44:35Zoai:ri.conicet.gov.ar:11336/239698instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:44:36.001CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
title |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
spellingShingle |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds Cardoso, Isolda Eugenia CHARACTERISTICALLY SOLVABLE LIE ALGEBRA NILMANIFOLD LEFT-INVARIANT METRIC INDEX OF SYMMETRY DISTRIBUTION OF SYMMETRY |
title_short |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
title_full |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
title_fullStr |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
title_full_unstemmed |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
title_sort |
The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
dc.creator.none.fl_str_mv |
Cardoso, Isolda Eugenia Cosgaya, Ana Reggiani, Silvio Nicolás |
author |
Cardoso, Isolda Eugenia |
author_facet |
Cardoso, Isolda Eugenia Cosgaya, Ana Reggiani, Silvio Nicolás |
author_role |
author |
author2 |
Cosgaya, Ana Reggiani, Silvio Nicolás |
author2_role |
author author |
dc.subject.none.fl_str_mv |
CHARACTERISTICALLY SOLVABLE LIE ALGEBRA NILMANIFOLD LEFT-INVARIANT METRIC INDEX OF SYMMETRY DISTRIBUTION OF SYMMETRY |
topic |
CHARACTERISTICALLY SOLVABLE LIE ALGEBRA NILMANIFOLD LEFT-INVARIANT METRIC INDEX OF SYMMETRY DISTRIBUTION OF SYMMETRY |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry. Fil: Cardoso, Isolda Eugenia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina Fil: Cosgaya, Ana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina |
description |
A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry. |
publishDate |
2024 |
dc.date.none.fl_str_mv |
2024-05 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/239698 Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás; The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds; Cornell University; ArXiv.org; 2024; 5-2024; 1-24 2331-8422 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/239698 |
identifier_str_mv |
Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás; The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds; Cornell University; ArXiv.org; 2024; 5-2024; 1-24 2331-8422 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2404.19177 info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2404.19177 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Cornell University |
publisher.none.fl_str_mv |
Cornell University |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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1844613403388149760 |
score |
13.070432 |