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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Detalles Bibliográficos
Autor principal: Rodríguez Valencia, Edwin Alejandro
Formato: article
Lenguaje:Inglés
Publicado: 2022
Materias:
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 Ver origen
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Sumario: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.