Results 1 to 10 of about 96,287 (28)

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
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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
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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
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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

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.
arxiv   +1 more source

Maximally non-integrable almost complex structures: an $h$-principle and cohomological properties [PDF]

Selecta Mathematica New Series 28, 83 (2022), 2021
We study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an $h$-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension $2n\geq 10$ (respectively $\geq 6$) admit a almost complex structure whose Nijenhuis tensor has maximal rank everywhere (resp.
arxiv   +1 more source

On hypercomplex pseudo-Hermitian manifolds [PDF]

Trends in Complex Analysis, Differential Geometry and Mathematical Physics, World Sci. Publ., Singapore, 2003, 51-62, 2008
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal invariance and the conformal equivalence of the basic types manifolds are studied.
arxiv   +1 more source

Invariant Tensors under the Twin Interchange of Norden Metrics on Almost Complex Manifolds [PDF]

Results in Mathematics, 1-18, 30 May 2015, 2015
The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e.
arxiv   +1 more source

Complex submanifolds of almost complex Euclidean spaces [PDF]

Quart. J. Math. 61 (2010), 401-405, 2009
We prove that a compact Riemann surface can be realized as a pseudo-holomorphic curve of $(\mathbb{R}^4,J)$, for some almost complex structure $J$ if and only if it is an elliptic curve. Furthermore we show that any (almost) complex $2n$-torus can be holomorphically embedded in $(\mathbb{R}^{4n},J)$ for a suitable almost complex structure $J$.
arxiv   +1 more source

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--
arxiv   +1 more source