A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types

We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilman...

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Autores principales:	Latorre Adela, Ugarte Luis, Villacampa Raquel
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2018
Materias:	nilmanifold nilpotent lie algebra complex structure hermitian metric homotopy theory minimal model 55p62 17b30 53c55 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a4ae4455916a4e3bb7c7d792c1ce7091
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id	oai:doaj.org-article:a4ae4455916a4e3bb7c7d792c1ce7091
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spelling	oai:doaj.org-article:a4ae4455916a4e3bb7c7d792c1ce70912021-12-02T17:14:47ZA Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types2300-744310.1515/coma-2018-0004https://doaj.org/article/a4ae4455916a4e3bb7c7d792c1ce70912018-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2018-0004https://doaj.org/toc/2300-7443We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.Latorre AdelaUgarte LuisVillacampa RaquelDe Gruyterarticlenilmanifoldnilpotent lie algebracomplex structurehermitian metrichomotopy theoryminimal model55p6217b3053c55MathematicsQA1-939ENComplex Manifolds, Vol 5, Iss 1, Pp 89-102 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	nilmanifold nilpotent lie algebra complex structure hermitian metric homotopy theory minimal model 55p62 17b30 53c55 Mathematics QA1-939
spellingShingle	nilmanifold nilpotent lie algebra complex structure hermitian metric homotopy theory minimal model 55p62 17b30 53c55 Mathematics QA1-939 Latorre Adela Ugarte Luis Villacampa Raquel A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types
description	We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.
format	article
author	Latorre Adela Ugarte Luis Villacampa Raquel
author_facet	Latorre Adela Ugarte Luis Villacampa Raquel
author_sort	Latorre Adela
title	A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types
title_short	A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types
title_full	A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types
title_fullStr	A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types
title_full_unstemmed	A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types
title_sort	family of complex nilmanifolds with in finitely many real homotopy types
publisher	De Gruyter
publishDate	2018
url	https://doaj.org/article/a4ae4455916a4e3bb7c7d792c1ce7091
work_keys_str_mv	AT latorreadela afamilyofcomplexnilmanifoldswithinfinitelymanyrealhomotopytypes AT ugarteluis afamilyofcomplexnilmanifoldswithinfinitelymanyrealhomotopytypes AT villacamparaquel afamilyofcomplexnilmanifoldswithinfinitelymanyrealhomotopytypes AT latorreadela familyofcomplexnilmanifoldswithinfinitelymanyrealhomotopytypes AT ugarteluis familyofcomplexnilmanifoldswithinfinitelymanyrealhomotopytypes AT villacamparaquel familyofcomplexnilmanifoldswithinfinitelymanyrealhomotopytypes
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A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types

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