Invariants of complex structures on nilmanifolds
Fil: Rodríguez Valencia, Edwin Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
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| Format: | publishedVersion |
| Language: | eng |
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2022
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| Online Access: | http://hdl.handle.net/11086/22155 http://dx.doi.org/10.5817/AM2015-1-27 |
| _version_ | 1801216667747876864 |
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| author | Rodríguez Valencia, Edwin Alejandro |
| author_facet | Rodríguez Valencia, Edwin Alejandro |
| author_sort | Rodríguez Valencia, Edwin Alejandro |
| collection | Repositorio Digital Universitario |
| description | Fil: Rodríguez Valencia, Edwin Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. |
| format | publishedVersion |
| id | rdu-unc.22155 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2022 |
| record_format | dspace |
| spelling | rdu-unc.221552022-10-13T11:08:30Z Invariants of complex structures on nilmanifolds Rodríguez Valencia, Edwin Alejandro Complex Nilmanifolds Nilpotent Lie groups Minimal metrics Pfaffian forms publishedVersion Fil: Rodríguez Valencia, Edwin Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Rodríguez Valencia, Edwin Alejandro. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Rodríguez Valencia, Edwin Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. 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. publishedVersion Fil: Rodríguez Valencia, Edwin Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Rodríguez Valencia, Edwin Alejandro. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Rodríguez Valencia, Edwin Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Matemática Pura 2022-01-13T15:09:11Z 2022-01-13T15:09:11Z 2015 article http://hdl.handle.net/11086/22155 http://dx.doi.org/10.5817/AM2015-1-27 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Electrónico y/o Digital eISSN 1212-5059 |
| spellingShingle | Complex Nilmanifolds Nilpotent Lie groups Minimal metrics Pfaffian forms Rodríguez Valencia, Edwin Alejandro Invariants of complex structures on nilmanifolds |
| title | 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_short | Invariants of complex structures on nilmanifolds |
| title_sort | invariants of complex structures on nilmanifolds |
| topic | Complex Nilmanifolds Nilpotent Lie groups Minimal metrics Pfaffian forms |
| url | http://hdl.handle.net/11086/22155 http://dx.doi.org/10.5817/AM2015-1-27 |
| work_keys_str_mv | AT rodriguezvalenciaedwinalejandro invariantsofcomplexstructuresonnilmanifolds |