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Search: All articles in the CMB digital archive with keyword Hermitian

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1. CMB Online first

Zhang, Zheng
On motivic realizations of the canonical Hermitian variations of Hodge structure of Calabi-Yau type over type $D^{\mathbb H}$ domains
Let $\mathcal{D}$ be the irreducible Hermitian symmetric domain of type $D_{2n}^{\mathbb{H}}$. There exists a canonical Hermitian variation of real Hodge structure $\mathcal{V}_{\mathbb{R}}$ of Calabi-Yau type over $\mathcal{D}$. This short note concerns the problem of giving motivic realizations for $\mathcal{V}_{\mathbb{R}}$. Namely, we specify a descent of $\mathcal{V}_{\mathbb{R}}$ from $\mathbb{R}$ to $\mathbb{Q}$ and ask whether the $\mathbb{Q}$-descent of $\mathcal{V}_{\mathbb{R}}$ can be realized as sub-variation of rational Hodge structure of those coming from families of algebraic varieties. When $n=2$, we give a motivic realization for $\mathcal{V}_{\mathbb{R}}$. When $n \geq 3$, we show that the unique irreducible factor of Calabi-Yau type in $\mathrm{Sym}^2 \mathcal{V}_{\mathbb{R}}$ can be realized motivically.

Keywords:variations of Hodge structure, Hermitian symmetric domain
Categories:14D07, 32G20, 32M15

2. CMB 2017 (vol 60 pp. 807)

Liu, Zhongyun; Qin, Xiaorong; Wu, Nianci; Zhang, Yulin
The Shifted Classical Circulant and Skew Circulant Splitting Iterative Methods for Toeplitz Matrices
It is known that every Toeplitz matrix $T$ enjoys a circulant and skew circulant splitting (denoted by CSCS) i.e., $T=C-S$ with $C$ a circulant matrix and $S$ a skew circulant matrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive definite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss-Seidel (GS) iterative methods if the CSCS is convergent, and that there is always a constant $\alpha$ such that the shifted CSCS iteration converges much faster than the Gauss-Seidel iteration, no matter whether the CSCS itself is convergent or not.

Keywords:Hermitian positive definite, CSCS splitting, Gauss-Seidel splitting, iterative method, Toeplitz matrix
Categories:15A23, 65F10, 65F15

3. CMB 2015 (vol 58 pp. 241)

Botelho, Fernanda
Isometries and Hermitian Operators on Zygmund Spaces
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.

Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries
Categories:46E15, 47B15, 47B38

4. CMB 2011 (vol 56 pp. 173)

Sahin, Bayram
Semi-invariant Submersions from Almost Hermitian Manifolds
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semi-invariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.

Keywords:Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion
Categories:53B20, 53C43

5. CMB 2011 (vol 54 pp. 396)

Cho, Jong Taek; Inoguchi, Jun-ichi; Lee, Ji-Eun
Parabolic Geodesics in Sasakian $3$-Manifolds
We give explicit parametrizations for all parabolic geodesics in 3-dimensional Sasakian space forms.

Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds

6. CMB 2009 (vol 52 pp. 18)

Chinea, Domingo
Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds
In this paper we study holomorphic maps between almost Hermitian manifolds. We obtain a new criterion for the harmonicity of such holomorphic maps, and we deduce some applications to horizontally conformal holomorphic submersions.

Keywords:almost Hermitian manifolds, harmonic maps, harmonic morphism
Categories:53C15, 58E20

7. CMB 2007 (vol 50 pp. 113)

Li, ZhenYang; Zhang, Xi
Hermitian Harmonic Maps into Convex Balls
In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is a compact Hermitian manifold with non-empty boundary.

Keywords:Hermitian harmonic map, Hermitian manifold, convex ball
Categories:58E15, 53C07

8. CMB 2004 (vol 47 pp. 73)

Li, Ma; Dezhong, Chen
Systems of Hermitian Quadratic Forms
In this paper, we give some conditions to judge when a system of Hermitian quadratic forms has a real linear combination which is positive definite or positive semi-definite. We also study some related geometric and topological properties of the moduli space.

Keywords:hermitian quadratic form, positive definite, positive semi-definite

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