Invariants of complex structures on nilmanifolds
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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2022
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Acceso en línea: | http://hdl.handle.net/11086/22155 http://dx.doi.org/10.5817/AM2015-1-27 |
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I10-R14111086-22155 |
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Universidad Nacional de Córdoba |
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I-10 |
repository_str |
R-141 |
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Repositorio Digital Universitario (UNC) |
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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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1764820395308875778 |