Abstract:
For an arbitrary real nilpotent Lie algebra (nilmanifold) with an integrable complex structure, we propose an algorithm for constructing a special model of this nilmanifold that includes information on the complex structure. As a main application, we obtain a classification of eight-dimensional 2-generated nilpotent Lie algebras that admit an integrable complex structure. We also describe the moduli spaces of complex structures for each Lie algebra from the resulting classification list.
Citation:
D. V. Millionshchikov, “Minimal Model of a Nilmanifold and Moduli Space of Complex Structures”, Geometry, Topology, and Mathematical Physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday, Trudy Mat. Inst. Steklova, 325, Steklov Mathematical Institute of RAS, Moscow, 2024, 201–231; Proc. Steklov Inst. Math., 325 (2024), 188–217
\Bibitem{Mil24}
\by D.~V.~Millionshchikov
\paper Minimal Model of a Nilmanifold and Moduli Space of Complex Structures
\inbook Geometry, Topology, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 325
\pages 201--231
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4416}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\pages 188--217
\crossref{https://doi.org/10.1134/S0081543824020111}
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Linking options:
https://www.mathnet.ru/eng/tm4416
https://doi.org/10.4213/tm4416
https://www.mathnet.ru/eng/tm/v325/p201
This publication is cited in the following 1 articles:
Adela Latorre, Luis Ugarte, “Nilmanifolds with non-nilpotent complex structures and their pseudo-Kähler geometry”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 119:2 (2025)
Citation in format AMSBIB
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