相关论文: Riemannian and filamentary geometries..
I review some recent advances in methods to diagnose polarized radiation with which we may hope to explore the magnetism of the solar chromosphere and corona. These methods are based on the remarkable signatures that the radiatively induced…
The solar corona is highly structured by bunches of magnetic field lines forming either loops, or twisted flux ropes representing prominences/filaments, or very dynamic structures such as jets. The aim of this paper is to understand the…
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian…
The solar surface and atmosphere are highly dynamic plasma environments, which evolve over a wide range of temporal and spatial scales. Large-scale eruptions, such as coronal mass ejections, can be accelerated to millions of kilometres per…
Solar filaments show the position of large scale polarity inversion lines and are used for the reconstruction of large-scale solar magnetic field structure on the basis of H{\alpha} synoptic charts for the periods when magnetographic…
We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
Filaments and coronal holes, two principal features observed in the solar corona are sources of space weather variations. Filament formation is closely associated with polarity inversion lines (PIL) on the solar photosphere which separate…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
In this study, we describe and evaluate shape measures for distinguishing between coronal holes and filament channels as observed in Extreme Ultraviolet (EUV) images of the Sun. For a set of well-observed coronal hole and filament channel…
Two of the most widely observed and yet most puzzling features of the Sun's magnetic field are coronal loops that are smooth and laminar and prominences/filaments that are strongly sheared. These two features would seem to be quite…
An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…
The Riemannian geometry of elastica in one and two dimensions is considered. An example is given of the deflexion or Frenet curvature of the elastic filament rod where the Riemannian curvature vanishes, since the curve is one dimensional.…
The global structure of solar corona observed in optical window is governed by the global magnetic field with different characteristics over solar activity cycle. Ludendorff flattening index becomes a popular measure of the global structure…
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the…
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.
We review the coronal visible and infrared lines, collecting previous observations, and comparing, whenever available, observed radiances with those predicted by various models: the quiet Sun, a moderately active Sun, and an active region…
The morphology of molecular clouds is crucial for understanding their origin and evolution. In this work, we investigate the morphology of the filamentary molecular clouds (filaments for short) using a portion of the $^{12}\text{CO}…
We present an overview of the physical mechanisms responsible for the coronal polarization at different wavelength regimes. We also review different techniques using coronal polarization to determine various quantities necessary for…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…