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Mathematics > Differential Geometry

arXiv:1410.3610 (math)
[Submitted on 14 Oct 2014 (v1), last revised 10 May 2015 (this version, v2)]

Title:Tamed symplectic structures on compact solvmanifolds of completely solvable type

Authors:Anna Fino, Hisashi Kasuya
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Abstract:A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a Kähler structure if and only if it is a complex torus. We show more in general that a compact solvmanifold $M$ of completely solvable type endowed with an invariant complex structure $J$ admits a symplectic form taming J if and only if $M$ is a complex torus. This result generalizes the one obtained in [7] for nilmanifolds.
Comments: 7 pages; to appear in Annali della Scuola Normale Superiore
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:1410.3610 [math.DG]
  (or arXiv:1410.3610v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1410.3610

Submission history

From: Anna Fino [view email]
[v1] Tue, 14 Oct 2014 08:28:59 UTC (8 KB)
[v2] Sun, 10 May 2015 15:46:01 UTC (9 KB)
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