Symplectic structures on Heisenberg-type nilmanifolds

Isabel Dotti; Paulo Tirao

doi:10.1007/s002291020383

Symplectic structures on Heisenberg-type nilmanifolds

Isabel Dotti, Paulo Tirao

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We use cohomological methods to study the existence of symplectic structures on nilmanifolds associated to two-step nilpotent Lie groups. We construct a new family of symplectic nilmanifolds with building blocks the quaternionic analogue of the Heisenberg group, determining the dimension of the space of all left invariant symplectic structures. Such structures can not be Kählerian. Also, we prove that the nilmanifolds associated to H type groups are not symplectic unless they correspond to the classical Heisenberg groups.

Original language	English
Pages (from-to)	383-401
Number of pages	19
Journal	Manuscripta Mathematica
Volume	102
Issue number	3
DOIs	https://doi.org/10.1007/s002291020383
State	Published - Jul 2000
Externally published	Yes

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title = "Symplectic structures on Heisenberg-type nilmanifolds",

abstract = "We use cohomological methods to study the existence of symplectic structures on nilmanifolds associated to two-step nilpotent Lie groups. We construct a new family of symplectic nilmanifolds with building blocks the quaternionic analogue of the Heisenberg group, determining the dimension of the space of all left invariant symplectic structures. Such structures can not be K{\"a}hlerian. Also, we prove that the nilmanifolds associated to H type groups are not symplectic unless they correspond to the classical Heisenberg groups.",

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N2 - We use cohomological methods to study the existence of symplectic structures on nilmanifolds associated to two-step nilpotent Lie groups. We construct a new family of symplectic nilmanifolds with building blocks the quaternionic analogue of the Heisenberg group, determining the dimension of the space of all left invariant symplectic structures. Such structures can not be Kählerian. Also, we prove that the nilmanifolds associated to H type groups are not symplectic unless they correspond to the classical Heisenberg groups.

AB - We use cohomological methods to study the existence of symplectic structures on nilmanifolds associated to two-step nilpotent Lie groups. We construct a new family of symplectic nilmanifolds with building blocks the quaternionic analogue of the Heisenberg group, determining the dimension of the space of all left invariant symplectic structures. Such structures can not be Kählerian. Also, we prove that the nilmanifolds associated to H type groups are not symplectic unless they correspond to the classical Heisenberg groups.

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U2 - 10.1007/s002291020383

DO - 10.1007/s002291020383

M3 - 文章

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VL - 102

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JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

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ER -

Symplectic structures on Heisenberg-type nilmanifolds

Abstract

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