Results 1 to 10 of about 4,690,894 (89)
On Lie groups as quasi-Kähler manifolds with Killing Norden metric [PDF]
Adv. Geom. 8 (2008), 343-352, 2007 A 6-parametric family of 6--dimensional quasi-K\"ahler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically.
Ganchev A. V +5 more
arxiv +3 more sources
The complex geometry of a hypothetical complex structure on $S^6$ [PDF]
Differential Geom. Appl. 57 (2018), 121-137, 2019 This article is a survey about or introduction to certain aspects of the complex geometry of a hypothetical complex structure on the six-sphere. We discuss a result of Peternell--Campana--Demailly on the algebraic dimension of a hypothetical complex six-sphere and give some examples. We also give an overview over an application of Huckleberry--Kebekus--
Lehn, Christian +2 more
arxiv +3 more sources
The complex geometry of two exceptional flag manifolds [PDF]
Annali di Matematica Pura ed Applicata 199 (2020), 2227--2241, 2019 We discuss the complex geometry of two complex five-dimensional K\"ahler manifolds which are homogeneous under the exceptional Lie group $G_2$. For one of these manifolds rigidity of the complex structure among all K\"ahlerian complex structures was proved by Brieskorn, for the other one we prove it here.
Kotschick, Dieter, Thung, D. K.
arxiv +5 more sources
Totally real immersions of surfaces [PDF]
Transactions of the American Mathematical Society 362 (2010), no.
1, pp. 53-115, 2006 Totally real immersions $f$ of a closed real surface $\Sigma$ in an almost complex surface $M$ are completely classified, up to homotopy through totally real immersions, by suitably defined homotopy classes $\frak{M}(f)$ of mappings from $\Sigma$ into a specific real 5-manifold $E(M)$, while $\frak{M}(f)$ themselves are subject to a single cohomology ...
Derdzinski, Andrzej +1 more
arxiv +5 more sources
On manifold-like polyfolds as differential geometrical objects with applications in complex geometry [PDF]
arXivWe argue for more widespread use of manifold-like polyfolds (M-polyfolds) as differential geometric objects. M-polyfolds possess a distinct advantage over differentiable manifolds, enabling a smooth and local change of dimension. To establish their utility, we introduce tensors and prove the existence of Riemannian metrics, symplectic structures, and ...
Czyż, Rafał\ +3 more
arxiv +2 more sources
An a priori C0-estimate for the Fu-Yau equation on compact almost astheno-Kähler manifolds
Complex Manifolds, 2022 We investigate the Fu-Yau equation on compact almost astheno-Kähler manifolds and show an a priori C0-estiamte for a smooth solution of the equation.
Kawamura Masaya
doaj +1 more source
Estimates for a function on almost Hermitian manifolds
Complex Manifolds, 2021 We study some estimates for a real-valued smooth function φ on almost Hermitian manifolds. In the present paper, we show that ∂∂∂̄ φ and ∂̄∂∂̄ φ can be estimated by the gradient of the function φ.
Kawamura Masaya
doaj +1 more source
On a k-th Gauduchon almost Hermitian manifold
Complex Manifolds, 2022 We characterize the k-th Gauduchon condition and by applying its characterization, we reprove that a compact k-th Gauduchon, semi-Kähler manifold becomes quasi-Kähler, which tells us that in particular, a compact almost pluriclosed, semi-Kähler manifold ...
Kawamura Masaya
doaj +1 more source
Hodge-de Rham numbers of almost complex 4-manifolds [PDF]
, 2022 We introduce and study Hodge-de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general setting, and ...
Cirici, Joana, Wilson, Scott O.
core +2 more sources
Left invariant nearly pseudo-Kähler structures and the tangent lie group [PDF]
Publ. Math. Debrecen 105 (2024) no. 3-4, 515-522, 2023 Let $G$ be a Lie group, and let $(g,J)$ be a left invariant almost pseudo-Hermitian structure on $G$. It is shown that if $(g,J)$ is also nearly pseudo-K\"{a}hler, then the tangent bundle $TG$ (with its natural Lie group structure induced from $G$) admits a left-invariant nearly pseudo-K\"{a}hler structure.
arxiv +1 more source