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dc.contributor.author
Lauret, Jorge Ruben
dc.contributor.author
Will, Cynthia Eugenia
dc.date.available
2023-12-19T13:28:02Z
dc.date.issued
2023-03
dc.identifier.citation
Lauret, Jorge Ruben; Will, Cynthia Eugenia; Harmonic 3-Forms on Compact Homogeneous Spaces; Springer; The Journal Of Geometric Analysis; 33; 6; 3-2023; 1-39
dc.identifier.issn
1050-6926
dc.identifier.uri
http://hdl.handle.net/11336/220765
dc.description.abstract
The third real de Rham cohomology of compact homogeneous spaces is studied. Given M= G/ K with G compact semisimple, we first show that each bi-invariant symmetric bilinear form Q on g such that Q| k×k= 0 naturally defines a G-invariant closed 3-form HQ on M, which plays the role of the so called Cartan 3-form Q([· , ·] , ·) on the compact Lie group G. Indeed, every class in H3(G/ K) has a unique representative HQ. Second, focusing on the class of homogeneous spaces with the richest third cohomology (other than Lie groups), i.e., b3(G/ K) = s- 1 if G has s simple factors, we give the conditions to be fulfilled by Q and a given G-invariant metric g in order for HQ to be g-harmonic, in terms of algebraic invariants of G/K. As an application, we obtain that any 3-form HQ is harmonic with respect to the standard metric, although for any other normal metric, there is only one HQ up to scaling which is harmonic. Furthermore, among a suitable (2 s- 1) -parameter family of G-invariant metrics, we prove that the same behavior occurs if k is abelian: either every HQ is g-harmonic (this family of metrics depends on s parameters) or there is a unique g-harmonic 3-form HQ (up to scaling). In the case when k is not abelian, the special metrics for which every HQ is g-harmonic depend on 3 parameters.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
3-FORM
dc.subject
HARMONIC
dc.subject
HOMOGENEOUS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Harmonic 3-Forms on Compact Homogeneous Spaces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-12-19T12:34:22Z
dc.journal.volume
33
dc.journal.number
6
dc.journal.pagination
1-39
dc.journal.pais
Alemania
dc.description.fil
Fil: Lauret, Jorge Ruben. 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
dc.description.fil
Fil: Will, Cynthia Eugenia. 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
dc.journal.title
The Journal Of Geometric Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s12220-023-01221-0
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s12220-023-01221-0
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