The complex 2-sphere in ℂ3 and Schrödinger flows

Ding, Qi; Zhong, Shiping

doi:10.1007/s11425-018-9350-0

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…This cross product is completely similar to that in R 3 , though the components of u and v are complex numbers (see [35]). The special complex structure on CS 2 (1), denoted by J, is different from the canonical one induced from C 3 but compatible with the Norden metric on CS 2 (1), which is defined by the following formula (see [26] for details): for p ∈ CS 2 (1),…”

Section: The Case Of the Complex 3-space Cmentioning

confidence: 99%

On the vortex filament in 3-spaces and its generalizations

Ding

Zhong

2021

Sci. China Math.

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In this article, we devote to a mathematical survey on the theory of the vortex filament in 3dimensional spaces and its generalizations. We shall present some effective geometric tools applied in the study, such as the Schrödinger flow, the geometric Korteweg-de Vries (KdV) flow and the generalized bi-Schrödinger flow, as well as the complex and para-complex structures. It should be mentioned that the investigation in the imaginary part of the octonions looks very fascinating, since it relates to almost complex structures and the G 2 structure on S 6 . As a new result in this survey, we describe the equation of generalized bi-Schrödinger flows from R 1 into a Riemannian surface.

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Section: The Case Of the Complex 3-space Cmentioning

confidence: 99%

On the vortex filament in 3-spaces and its generalizations

Ding

Zhong

2021

Sci. China Math.

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“…This motivates the introduce in geometry the concept of Schrödinger flows (or maps) (see [8,27] or [4]). It is proved in [10] that CLL (1.6) is exactly the equation of Schrödinger flows from R 1 to the complex 2-sphere CS 2 (1) → C 3 .…”

Section: Motion Of Complex Curves In Cmentioning

confidence: 99%

“…) of the NLS system (1.5) are unique (e.g. refer to [10]). Returning to the complex moving curves X(x, t) in C 3 , we have the following conclusion.…”

Section: Geometric Interpretation Of Nnlsmentioning

confidence: 99%

“…Hence NNLS arises from the motion (1.4) of complex curves just with the initial-data being suitably restricted. By using gauge equivalent way, Ding et al in [10] have given an accurate characterization of the gauge-equivalent magnetic structure of NNLS, but here we give the direct interrelations between NNLS and the motion of complex curves in C 3 . Finally, by using Murugesh and Balakrishnana's unified formalism [23], any given solution of the NLS system (1.5) gets associated with three distinct complex curve evolutions, that is the tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third satisfy to CLL (1.6).…”

Section: Introductionmentioning

confidence: 99%

“…(1.1). In [10,13], the NLS system (1.5) is gauge equivalent to CLL (1.6) and vice versa. Here, by using the viewpoint of complex moving curves in C 3 , Eq.…”

Section: Introductionmentioning

confidence: 99%

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A motion of complex curves in $C^3$ and the nonlocal nonlinear Schrödinger equation

Zhong¹

2018

J. Nonlinear Sci. Appl.

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Exploring Late‐Time Cosmic Acceleration with Eos Parameterizations in Horava‐Lifshitz Gravity via Baryon Acoustic Oscillations

Khurana,

Chaudhary,

Debnath

et al. 2024

Fortschritte der Physik

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In this study, the framework of Horava‐Lifshitz gravity to model the Universe's dark matter and dark energy (DE) components is adopted. Specifically, two recent parametrizations for DE models: the CBDRM‐type and CADMM‐type parameterizations is considered. In the analysis, the Hubble parameter is explicitly expressed, denoted as , for these two distinct dark energy models. By doing so, investigate and quantify the accelerated cosmic expansion rate characterizing the late‐time Universe is aimed. This study uses a wide range of datasets. This dataset consists of recent measurements of baryon acoustic oscillations (BAOs) collected over a period of 22 years with the Cosmic Chronometers (CC) dataset, Type Ia supernovae (SNIa) dataset, the Hubble diagram of gamma‐ray bursts (GRBs), quasars (Q), and the latest measurement of the Hubble constant (R22). Consequently, a crucial aspect of this study by plotting the vs. H0 plane is presented. In the context of the ΛCDM model, after incorporating all the datasets, including the R22 prior, the following results: H0 = 71.674089 ± 0.734089 and is obtained. For the CBDRM model, H0 = 72.355058 ± 1.004604 and is found. In the case of the CADMM model, the analysis yields H0 = 72.347804 ± 0.923328 and . Cosmographic analyses for both of the proposed parameterizations in comparison to the ΛCDM paradigm are conducted. Additionally, Diagnostic tests to investigate the evolution of both models is applied. Finally, the Information Criteria test demonstrates that the ΛCDM model emerges as the preferred choice among the models is considered.

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The complex 2-sphere in ℂ3 and Schrödinger flows

Cited by 8 publications

References 30 publications

On the vortex filament in 3-spaces and its generalizations

On the vortex filament in 3-spaces and its generalizations

A motion of complex curves in $C^3$ and the nonlocal nonlinear Schrödinger equation

Exploring Late‐Time Cosmic Acceleration with Eos Parameterizations in Horava‐Lifshitz Gravity via Baryon Acoustic Oscillations

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