Compact complex non-Kähler manifolds associated with totally real reciprocal units

Miebach, Christian; Oeljeklaus, Karl

doi:10.1007/s00209-022-03010-x

Cited by 3 publications

(2 citation statements)

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“…Regarding {α, β} as a global C ∞ -frame of (1, 0)-forms, we have a left-invariant complex structure on H. Now, consider G = H d . Miebach and Oeljeklaus construct in [MO22] a lattice Γ in G corresponding to a totally real number field K of degree d satisfying certain conditions. From this, we get the compact complex manifold X := G/Γ with a global C ∞ -frame {α 1 , .…”

Section: Partial Hyperbolicity Of Miebach-oeljeklaus Manifoldsmentioning

confidence: 99%

“…In §3, we exhibit four classes of compact complex manifolds that have partial hyperbolicity properties: all Oeljeklaus-Toma manifolds [OT05] (cf. Proposition 3.1), certain manifolds constructed very recently by Miebach and Oeljeklaus in [MO22] (cf. Proposition 3.5), a certain class of complex parallelisable solvmanifolds similar to those constructed in [Kas17] (cf.…”

Section: Introductionmentioning

confidence: 99%

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Some properties of balanced hyperbolic compact complex manifolds

Marouani

Popovici

2022

Int. J. Math.

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We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the [Formula: see text] harmonic spaces on the universal cover of these manifolds. Other results include a Hard Lefschetz-type theorem for certain compact complex balanced manifolds and the non-existence of certain [Formula: see text] currents on the universal covering space of a balanced hyperbolic manifold.

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Section: Partial Hyperbolicity Of Miebach-oeljeklaus Manifoldsmentioning

confidence: 99%