p-Kähler and balanced structures on nilmanifolds with nilpotent complex structures

Sferruzza, Tommaso; Tardini, Nicoletta

doi:10.1007/s10455-022-09867-9

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…Some obstructions to their existence were determined in [15], where the authors extended the definition to non-integrable almost complex manifolds, and in [23], on nilmanifolds with nilpotent complex structures. In [5], Alessandrini and Bassanelli conjectured that if X is p-Kähler then it is q-Kähler for all p ≤ q < n.…”

Section: Introductionmentioning

confidence: 99%

Exact G$$_{\mathbf{2}}$$-structures on compact quotients of Lie groups

Fino

Martín‐Merchán

Raffero

2022

Annali di Matematica

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We show that the compact quotient $$\Gamma \backslash {\mathrm G}$$ Γ \ G of a seven-dimensional simply connected Lie group $${\mathrm G}$$ G by a co-compact discrete subgroup $$\Gamma \subset {\mathrm G}$$ Γ ⊂ G does not admit any exact $${\mathrm G}_2$$ G 2 -structure which is induced by a left-invariant one on $${\mathrm G}$$ G .

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Section: Introductionmentioning

confidence: 99%

Exact G$$_{\mathbf{2}}$$-structures on compact quotients of Lie groups

Fino

Martín‐Merchán

Raffero

2022

Annali di Matematica

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A note on p-Kähler structures on compact quotients of Lie groups

Fino,

Mainenti

2024

Annali di Matematica

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A p-Kähler structure on a complex manifold of complex dimension n is given by a d-closed transverse real (p, p)-form. In the paper, we study the existence of p-Kähler structures on compact quotients of simply connected Lie groups by discrete subgroups endowed with an invariant complex structure. In particular, we discuss the existence of p-Kähler structures on nilmanifolds, with a focus on the case $$p =2$$ p = 2 and complex dimension $$n = 4$$ n = 4 . Moreover, we prove that a $$(n-2)$$ ( n - 2 ) -Kähler almost abelian solvmanifold of complex dimension $$n\ge 3$$ n ≥ 3 has to be Kähler.

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Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics

Latorre,

Ugarte,

Villacampa

2024

Ann Glob Anal Geom

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In this paper we focus on the interplay between the behaviour of the Frölicher spectral sequence and the existence of special Hermitian metrics on the manifold, such as balanced, SKT or generalized Gauduchon. The study of balanced metrics on nilmanifolds endowed with strongly non-nilpotent complex structures allows us to provide infinite families of compact balanced manifolds with Frölicher spectral sequence not degenerating at the second page. Moreover, this result is extended to non-degeneration at any arbitrary page. Similar results are obtained for the Frölicher spectral sequence of compact generalized Gauduchon manifolds. We also find a compact SKT manifold whose Frölicher spectral sequence does not degenerate at the second page, thus providing a counterexample to a conjecture by Popovici.

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p-Kähler and balanced structures on nilmanifolds with nilpotent complex structures

Cited by 3 publications

References 19 publications

Exact G$$_{\mathbf{2}}$$-structures on compact quotients of Lie groups

Exact G$$_{\mathbf{2}}$$-structures on compact quotients of Lie groups

A note on p-Kähler structures on compact quotients of Lie groups

Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics

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