Invariants of complex structures on nilmanifolds

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Let (N, J) be a simply connected 2n-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on N compatible with J to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the...

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Autor principal: Rodríguez Valencia, Edwin Alejandro
Formato: article
Lenguaje:Inglés
Publicado: 2022
Materias:
Complex
Nilmanifolds
Nilpotent Lie groups
Minimal metrics
Pfaffian forms
Acceso en línea:http://hdl.handle.net/11086/22155
http://dx.doi.org/10.5817/AM2015-1-27
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-22155
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Complex
Nilmanifolds
Nilpotent Lie groups
Minimal metrics
Pfaffian forms
spellingShingle Complex
Nilmanifolds
Nilpotent Lie groups
Minimal metrics
Pfaffian forms
Rodríguez Valencia, Edwin Alejandro
Invariants of complex structures on nilmanifolds
topic_facet Complex
Nilmanifolds
Nilpotent Lie groups
Minimal metrics
Pfaffian forms
description Let (N, J) be a simply connected 2n-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on N compatible with J to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving rise to a great deal of invariants. We show how to use a Riemannian invariant: the eigenvalues of the Ricci operator, polynomial invariants and discrete invariants to give an alternative proof of the pairwise non-isomorphism between the structures which have appeared in the classification of abelian complex structures on 6-dimensional nilpotent Lie algebras given in [1]. We also present some continuous families in dimension 8.
format article
author Rodríguez Valencia, Edwin Alejandro
author_facet Rodríguez Valencia, Edwin Alejandro
author_sort Rodríguez Valencia, Edwin Alejandro
title Invariants of complex structures on nilmanifolds
title_short Invariants of complex structures on nilmanifolds
title_full Invariants of complex structures on nilmanifolds
title_fullStr Invariants of complex structures on nilmanifolds
title_full_unstemmed Invariants of complex structures on nilmanifolds
title_sort invariants of complex structures on nilmanifolds
publishDate 2022
url http://hdl.handle.net/11086/22155
http://dx.doi.org/10.5817/AM2015-1-27
work_keys_str_mv AT rodriguezvalenciaedwinalejandro invariantsofcomplexstructuresonnilmanifolds
bdutipo_str Repositorios
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