Non-Kähler compact complex manifolds associated to number fields

Oeljeklaus, Karl; Toma, Matei

doi:10.5802/aif.2093

Cited by 107 publications

(212 citation statements)

References 2 publications

Supporting

Mentioning

211

Contrasting

Order By: Relevance

“…We now extend the above results to Oeljeklaus-Toma manifolds [OT05] with precisely one complex place and s real place. Note that this is the case when the existence of lcK metrics is known, [OT05, Proposition 2.9], see also [Vul14, Theorem 3.1].…”

Section: 4mentioning

confidence: 99%

“…We briefly recall their construction (see [OT05]) and their structure as solvmanifolds (see [Kas13, Section 6]).…”

Section: 4mentioning

confidence: 99%

“…Following the same pattern as [Bry88,Mat95,Yan96,Mer98,Gui01,Cav05,TY12a], we study ellipticHodge-theory, and we get some results concerning Poincaré dualities, see Proposition 2.3 and Theorem 2.4, and Hard Lefschetz Condition, see Theorem 2.6 and Theorem 2.7. Finally, we study some explicit examples, on nilmanifolds (Kodaira-Thurston surface [Kod64,Thu76]) and solvmanifolds (Inoue surfaces of type S + [Ino74], for which see also [Oti16], and OeljeklausToma manifolds [OT05]). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cohomologies of locally conformally symplectic manifolds and solvmanifolds

Angella¹,

Otiman²,

Tardini³

2017

Ann Glob Anal Geom

View full text Add to dashboard Cite

Abstract. We study the Morse-Novikov cohomology and its almostsymplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard Lefschetz Condition. We consider solvmanifolds and Oeljeklaus-Toma manifolds. In particular, we prove that Oeljeklaus-Toma manifolds with precisely one complex place, and under an additional arithmetic condition, satisfy the Mostow property. This holds in particular for the Inoue surface of type S 0 .

show abstract

Section: 4mentioning

confidence: 99%

“…We briefly recall their construction (see [OT05]) and their structure as solvmanifolds (see [Kas13, Section 6]).…”

Section: 4mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cohomologies of locally conformally symplectic manifolds and solvmanifolds

Angella¹,

Otiman²,

Tardini³

2017

Ann Glob Anal Geom

View full text Add to dashboard Cite

show abstract

“…The examples M s = (H s × C)/Γ given in 2.4 and described in [OT05] satisfy rank(M s ) = s, for any integer s ≥ 1.…”

Section: Presentations Of Locally Conformal Kähler Manifoldsmentioning

confidence: 99%

“…A very recent example of locally conformal Kähler manifold is described in [OT05]. For any integer s ≥ 1, the authors construct a group Γ acting freely and properly discontinously by biholomorphisms on H s ×C (where H denotes the upper-half complex plane).…”

Section: Presentations Of Locally Conformal Kähler Manifoldsmentioning

confidence: 99%

Reduction of Vaisman structures in complex and quaternionic geometry

Gini¹,

Parton

Piccinni

2006

Journal of Geometry and Physics

View full text Add to dashboard Cite

Abstract. We consider locally conformal Kähler geometry as an equivariant (homothetic) Kähler geometry: a locally conformal Kähler manifold is, up to equivalence, a pair (K, Γ) where K is a Kähler manifold and Γ a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kähler manifold (K, Γ) as the rank of a natural quotient of Γ, and prove its invariance under reduction. This equivariant point of view leads to a proof that locally conformal Kähler reduction of compact Vaisman manifolds produces Vaisman manifolds and is equivalent to a Sasakian reduction. Moreover we define locally conformal hyperkähler reduction as an equivariant version of hyperkähler reduction and in the compact case we show its equivalence with 3-Sasakian reduction. Finally we show that locally conformal hyperkähler reduction induces hyperkähler with torsion (HKT) reduction of the associated HKT structure and the two reductions are compatible, even though not every HKT reduction comes from a locally conformal hyperkähler reduction.

show abstract

Units in Number Fields Satisfying a Multiplicative Relation with Application to Oeljeklaus–Toma Manifolds

Dubickas

2021

Results Math

View full text Add to dashboard Cite

Non-Kähler compact complex manifolds associated to number fields

Cited by 107 publications

References 2 publications

Cohomologies of locally conformally symplectic manifolds and solvmanifolds

Cohomologies of locally conformally symplectic manifolds and solvmanifolds

Reduction of Vaisman structures in complex and quaternionic geometry

Units in Number Fields Satisfying a Multiplicative Relation with Application to Oeljeklaus–Toma Manifolds

Contact Info

Product

Resources

About