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Complex Manifolds

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

Adela Latorre
  • Corresponding author
  • Centro Universitario de la Defensa - I.U.M.A., Academia General Militar, Crta. de Huesca s/n. 50090 Zaragoza, Spain
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/ Luis Ugarte
  • Departamento de Matemáticas - I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain
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/ Raquel Villacampa
  • Centro Universitario de la Defensa - I.U.M.A., Academia General Militar, Crta. de Huesca s/n. 50090 Zaragoza, Spain
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Published Online: 2018-02-16 | DOI: https://doi.org/10.1515/coma-2018-0004

Abstract

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.

Keywords: Nilmanifold; Nilpotent Lie algebra; Complex structure; Hermitian metric; Homotopy theory; Minimal model

MSC 2010: 55P62; 17B30; 53C55

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About the article

Received: 2017-12-14

Accepted: 2018-01-30

Published Online: 2018-02-16


Citation Information: Complex Manifolds, Volume 5, Issue 1, Pages 89–102, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2018-0004.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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