Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds

Autores
Andrada, Adrián Marcelo; Tolcachier, Alejandro
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is well known that the product of two Sasakian manifolds carries a 2-parameter family of Hermitian structures (J_(a,b), g_(a,b)). We show in this article that the complex structure J_(a,b) is harmonic with respect to g_(a,b) , i.e. it is a critical point of the Dirichlet energy functional. Furthermore, we also determine when these Hermitian structures are locally conformally Kähler, balanced, strong Kähler with torsion, Gauduchon or k-Gauduchon (k ≥ 2). Finally, we study the Bismut connection associated to (J_(a,b), g_(a,b)) and we provide formulas for the Bismut-Ricci tensor Ric^B and the Bismut-Ricci form ρ^B . We show that these tensors vanish if and only if each Sasakian factor is η-Einstein with appropriate constants and we also exhibit some examples fulfilling these conditions, thus providing new examples of Calabi-Yau with torsion manifolds.
Fil: Andrada, Adrián Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Tolcachier, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
HERMITIAN MANIFOLD
SASAKIAN MANIFOLD
HARMONIC ALMOST COMPLX STRUCTURE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/248370
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Harmonic complex structures and special hermitian metrics on products of Sasakian manifoldsAndrada, Adrián MarceloTolcachier, AlejandroHERMITIAN MANIFOLDSASAKIAN MANIFOLDHARMONIC ALMOST COMPLX STRUCTUREhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1It is well known that the product of two Sasakian manifolds carries a 2-parameter family of Hermitian structures (J_(a,b), g_(a,b)). We show in this article that the complex structure J_(a,b) is harmonic with respect to g_(a,b) , i.e. it is a critical point of the Dirichlet energy functional. Furthermore, we also determine when these Hermitian structures are locally conformally Kähler, balanced, strong Kähler with torsion, Gauduchon or k-Gauduchon (k ≥ 2). Finally, we study the Bismut connection associated to (J_(a,b), g_(a,b)) and we provide formulas for the Bismut-Ricci tensor Ric^B and the Bismut-Ricci form ρ^B . We show that these tensors vanish if and only if each Sasakian factor is η-Einstein with appropriate constants and we also exhibit some examples fulfilling these conditions, thus providing new examples of Calabi-Yau with torsion manifolds.Fil: Andrada, Adrián Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Tolcachier, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaSpringer2024-04-16info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/248370Andrada, Adrián Marcelo; Tolcachier, Alejandro; Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds; Springer; The Journal Of Geometric Analysis; 34; 6; 16-4-2024; 1-331050-6926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-024-01620-xinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s12220-024-01620-xinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2301.09706info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:53:19Zoai:ri.conicet.gov.ar:11336/248370instacron: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 09:53:20.048CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
title Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
spellingShingle Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
Andrada, Adrián Marcelo
HERMITIAN MANIFOLD
SASAKIAN MANIFOLD
HARMONIC ALMOST COMPLX STRUCTURE
title_short Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
title_full Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
title_fullStr Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
title_full_unstemmed Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
title_sort Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds
dc.creator.none.fl_str_mv Andrada, Adrián Marcelo
Tolcachier, Alejandro
author Andrada, Adrián Marcelo
author_facet Andrada, Adrián Marcelo
Tolcachier, Alejandro
author_role author
author2 Tolcachier, Alejandro
author2_role author
dc.subject.none.fl_str_mv HERMITIAN MANIFOLD
SASAKIAN MANIFOLD
HARMONIC ALMOST COMPLX STRUCTURE
topic HERMITIAN MANIFOLD
SASAKIAN MANIFOLD
HARMONIC ALMOST COMPLX STRUCTURE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv It is well known that the product of two Sasakian manifolds carries a 2-parameter family of Hermitian structures (J_(a,b), g_(a,b)). We show in this article that the complex structure J_(a,b) is harmonic with respect to g_(a,b) , i.e. it is a critical point of the Dirichlet energy functional. Furthermore, we also determine when these Hermitian structures are locally conformally Kähler, balanced, strong Kähler with torsion, Gauduchon or k-Gauduchon (k ≥ 2). Finally, we study the Bismut connection associated to (J_(a,b), g_(a,b)) and we provide formulas for the Bismut-Ricci tensor Ric^B and the Bismut-Ricci form ρ^B . We show that these tensors vanish if and only if each Sasakian factor is η-Einstein with appropriate constants and we also exhibit some examples fulfilling these conditions, thus providing new examples of Calabi-Yau with torsion manifolds.
Fil: Andrada, Adrián Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Tolcachier, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description It is well known that the product of two Sasakian manifolds carries a 2-parameter family of Hermitian structures (J_(a,b), g_(a,b)). We show in this article that the complex structure J_(a,b) is harmonic with respect to g_(a,b) , i.e. it is a critical point of the Dirichlet energy functional. Furthermore, we also determine when these Hermitian structures are locally conformally Kähler, balanced, strong Kähler with torsion, Gauduchon or k-Gauduchon (k ≥ 2). Finally, we study the Bismut connection associated to (J_(a,b), g_(a,b)) and we provide formulas for the Bismut-Ricci tensor Ric^B and the Bismut-Ricci form ρ^B . We show that these tensors vanish if and only if each Sasakian factor is η-Einstein with appropriate constants and we also exhibit some examples fulfilling these conditions, thus providing new examples of Calabi-Yau with torsion manifolds.
publishDate 2024
dc.date.none.fl_str_mv 2024-04-16
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/11336/248370
Andrada, Adrián Marcelo; Tolcachier, Alejandro; Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds; Springer; The Journal Of Geometric Analysis; 34; 6; 16-4-2024; 1-33
1050-6926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/248370
identifier_str_mv Andrada, Adrián Marcelo; Tolcachier, Alejandro; Harmonic complex structures and special hermitian metrics on products of Sasakian manifolds; Springer; The Journal Of Geometric Analysis; 34; 6; 16-4-2024; 1-33
1050-6926
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-024-01620-x
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s12220-024-01620-x
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2301.09706
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/zip
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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score 13.070432

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