相关论文: Riemannian and filamentary geometries..

In this paper, we detail the scientific objectives and outline a strawman payload of the SOLAR sail Investigation of the Sun (SOLARIS). The science objectives are to study the 3D structure of the solar magnetic and velocity field, the…

We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

Solar filaments are cold and dense materials situated in magnetic dips, which show distinct radiation characteristics compared to the surrounding coronal plasma. They are associated with coronal sheared and twisted magnetic field lines.…

This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications…

The aim of this article is to present a comparative review of Riemannian and Finsler geometry. The structures of cut and conjugate loci on Riemannian manifolds have been discussed by many geometers including H. Busemann, M. Berger and W.…

Solar prominences and filaments (prominences projected against the solar disk) exhibit a large variety of fine structures which are well observed down to the resolution limit of ground-based telescopes. We describe the morphological aspects…

In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and…

In this review, I focus on the structure and evolution of the coronal magnetic fields modelled from observations. The development of instruments measuring the photospheric and chromospheric magnetic fields with a high spatial and time…

In this paper, we study biharmonic Riemannian submersions. We first derive bitension field of a general Riemannian submersion, we then use it to obtain biharmonic equations for Riemannian submersions with $1$-dimensional fibers and…

The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…

A number of authors have reported filaments connecting bright structures in high-resolution X-ray images, and in some cases these have been taken as evidence for a physical connection between the structures, which might be thought to…

In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields…

This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological structure of collapsed/non-collapsed…

Quiescent filaments are usually affected by internal and/or external perturbations triggering oscillations of different kinds. In particular, external large-scale coronal waves can perturb remote quiescent filaments leading to…

In the era of space exploration, coronal holes on the sun play a significant role due to their impact on satellites and aircraft through their open magnetic fields and increased solar wind emissions. This study employs computer vision…

We study bimodule quantum Riemannian geometries over the field $\Bbb F_2$ of two elements as the extreme case of a finite-field adaptation of noncommutative-geometric methods for physics. We classify all parallelisable such geometries for…

The solar corona, anomalously hot outer atmosphere of the Sun, is traditionally described by magnetohydrodynamic, fluid-like approach. Here we review some recent developments when, instead, a full kinetic description is used. It is shown…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

Filaments are one of the most common features in the solar atmosphere, and are of significance in solar, stellar and laboratory plasma physics. Using data from the Chinese H$\alpha$ Solar Explorer, the Solar Upper Transition Region Imager…