Hermitian structures on a class of almost nilpotent solvmanifolds
TLDR
In this article , the existence of invariant SKT, balanced and generalized Kähler structures on compact quotients Γ﹨G, where G is an almost nilpotent Lie group whose nilradical has one-dimensional commutator and Γ is a lattice of G, was investigated.About:
This article is published in Journal of Algebra.The article was published on 2022-11-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Commutator & Hermitian matrix.read more
Citations
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Compatibility of Balanced and SKT Metrics on Two-Step Solvable Lie Groups
Marco Freibert,Andrew Swann +1 more
TL;DR: In this paper , it was shown that a compact two-step complex manifold admits both a compatible SKT and a compatible balanced metric also admits a compatible Kähler metric, using the shear construction and classification results for 2-step solvable SKT Lie algebras from previous work.
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Locally conformal SKT structures
TL;DR: In this paper , a new type of Hermitian metric called locally conformal strong Kähler with torsion (LCSKT) is introduced, which is a conformal generalization of the SKT condition.
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Hermitian geometry of Lie algebras with abelian ideals of codimension 2
Yuqin Guo,Fangyang Zheng +1 more
Posted Content
Locally conformal SKT structures.
TL;DR: In this paper, a new type of Hermitian metric called locally conformal SKT (or shortly LCSKT) is introduced, where the Bismut torsion is closed.
References
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A local index theorem for non Kähler manifolds
TL;DR: On considere des conditions suffisantes pour qu'un theoreme d'indice local soit vrai pour un operateur de Dirac associe a une connexion qui ne coincide pas necessairement avec la connexions de Levi-Civita L
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Instantons, Poisson Structures and Generalized Kähler Geometry
TL;DR: In this paper, the authors construct bihermitian metrics on CP2 and CP1×CP1, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M.
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Bihermitian structures on complex surfaces
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On low-dimensional solvmanifolds
TL;DR: In this article, the authors consider the question of existence of lattices in solvable Lie groups up to dimension six and examine whether the corresponding solvmanifolds are formal, symplectic, Kaehler or (Hard) Lefschetz.