A Classification of Homogeneous Surfaces

1981 ◽  
Vol 33 (5) ◽  
pp. 1097-1110 ◽  
Author(s):  
A. T. Huckleberry ◽  
E. L. Livorni
Keyword(s):  
Automorphism Group ◽  
Homogeneous Space ◽  
Lie Group ◽  
Compact Complex Manifold ◽  
Coset Space ◽  
Left Coset ◽  
Detailed Classification ◽  
Dimensional Ball ◽  
Lie Subgroup

Throughout this paper a surface is a 2-dimensional (not necessarily compact) complex manifold. A surface X is homogeneous if a complex Lie group G of holomorphic transformations acts holomorphically and transitively on it. Concisely, X is homogeneous if it can be identified with the left coset space G/H, where if is a closed complex Lie subgroup of G. We emphasize that the assumption that G is a complex Lie group is an essential part of the definition. For example, the 2-dimensional ball B2 is certainly “homogeneous” in the sense that its automorphism group acts transitively. But it is impossible to realize B2 as a homogeneous space in the above sense. The purpose of this paper is to give a detailed classification of the homogeneous surfaces. We give explicit descriptions of all possibilities.

scholarly journals On the Automorphism Group of a Holomorphic Fiber Bundle over A Complex Space

1970 ◽  
Vol 37 ◽  
pp. 91-106 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Automorphism Group ◽  
Lie Group ◽  
Fiber Bundle ◽  
Complex Space ◽  
Automorphism Groups ◽  
Compact Complex Manifold ◽  
Compact Open Topology ◽  
Complex Spaces ◽  
Holomorphic Fiber Bundle ◽  
Holomorphic Automorphisms

In [8], A. Morimoto proved that the automorphism group of a holomorphic principal fiber bundle over a compact complex manifold has a structure of a complex Lie group with the compact-open topology. The purpose of this paper is to get similar results on the automorphism groups of more general types of locally trivial fiber spaces over complex spaces. We study automorphisms of a holomorphic fiber bundle over a complex space which has a complex space Y as the fiber and a (not necessarily complex Lie) group G of holomorphic automorphisms of Y as the structure group (see Definition 3. l).

ABSTRACT HARMONIC ANALYSIS OF RELATIVE CONVOLUTIONS OVER CANONICAL HOMOGENEOUS SPACES OF SEMIDIRECT PRODUCT GROUPS

2016 ◽  
Vol 101 (2) ◽  
pp. 171-187 ◽  
Author(s):  
ARASH GHAANI FARASHAHI
Keyword(s):  
Harmonic Analysis ◽  
Homogeneous Space ◽  
Semidirect Product ◽  
Homogeneous Spaces ◽  
Continuous Homomorphism ◽  
Compact Groups ◽  
Coset Space ◽  
Unified Approach ◽  
Left Coset ◽  
Semidirect Product Groups

This paper presents a structured study for abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups. Let $H,K$ be locally compact groups and $\unicode[STIX]{x1D703}:H\rightarrow \text{Aut}(K)$ be a continuous homomorphism. Let $G_{\unicode[STIX]{x1D703}}=H\ltimes _{\unicode[STIX]{x1D703}}K$ be the semidirect product of $H$ and $K$ with respect to $\unicode[STIX]{x1D703}$ and $G_{\unicode[STIX]{x1D703}}/H$ be the canonical homogeneous space (left coset space) of $G_{\unicode[STIX]{x1D703}}/H$. We present a unified approach to the harmonic analysis of relative convolutions over the canonical homogeneous space $G_{\unicode[STIX]{x1D703}}/H$.

scholarly journals On orbits of algebraic groups and Lie groups

1982 ◽  
Vol 25 (1) ◽  
pp. 1-28 ◽  
Author(s):  
R.W. Richardson
Keyword(s):  
Fixed Points ◽  
Homogeneous Space ◽  
Algebraic Group ◽  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Algebraic Groups ◽  
General Situation ◽  
Coset Space ◽  
Identity Component

In this paper we will be concerned with orbits of a closed subgroup Z of an algebraic group (respectively Lie group) G on a homogeneous space X for G. More precisely, let D be a closed subgroup of G and let X denote the coset space G/D. Let S be a subgroup of G and let Z denote (GS)0 the identity component of GS, the centralizer of S in G. We consider the orbits of Z on XS, the set of fixed points of S on X. We also treat the more general situation in which S is an algebraic group (respectively Lie group) which acts on G by automorphisms and acts on X compatibly with the action of G; again we consider the orbits of (GS)0 on XS.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification

PROPER ACTIONS ON SOME EXPONENTIAL SOLVABLE HOMOGENEOUS SPACES

2005 ◽  
Vol 16 (09) ◽  
pp. 941-955 ◽  
Author(s):  
ALI BAKLOUTI ◽  
FATMA KHLIF
Keyword(s):  
Maximal Subgroup ◽  
Homogeneous Space ◽  
Lie Group ◽  
Homogeneous Spaces ◽  
Intersection Property ◽  
Nilpotent Lie Group ◽  
Proper Actions ◽  
Simply Connected

Let G be a connected, simply connected nilpotent Lie group, H and K be connected subgroups of G. We show in this paper that the action of K on X = G/H is proper if and only if the triple (G,H,K) has the compact intersection property in both cases where G is at most three-step and where G is special, extending then earlier cases. The result is also proved for exponential homogeneous space on which acts a maximal subgroup.

On Flag Curvature of Homogeneous Randers Spaces

2013 ◽  
Vol 65 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Shaoqiang Deng ◽  
Zhiguang Hu
Keyword(s):  
Explicit Formula ◽  
Lie Group ◽  
Flag Curvature ◽  
Nilpotent Lie Group ◽  
Finsler Spaces ◽  
Rigidity Result ◽  
Randers Space ◽  
Negatively Curved

AbstractIn this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randersmetric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification

scholarly journals Analysis and Classification of Mitigation Tools against Cyberattacks in COVID-19 Era

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
George Iakovakis ◽  
Constantinos-Giovanni Xarhoulacos ◽  
Konstantinos Giovas ◽  
Dimitris Gritzalis
Keyword(s):  
Computer Networks ◽  
Risk Mitigation ◽  
Security Risks ◽  
Work From Home ◽  
Detailed Classification ◽  
Threat Intelligence ◽  
One Step ◽  
Automated Tools ◽  
Cyber Threat Intelligence

The COVID-19 outbreak has forced businesses to shift to an unprecedented “work from home” company environment. While this provides advantages for employees and businesses, it also leads to a multitude of shortcomings, most prevalent of which is the emergence of additional security risks. Previous to the outbreak, company computer networks were mainly confined within its facilities. The pandemic has now caused this network to “spread thin,” as the majority of employees work remotely. This has opened up a variety of new vulnerabilities, as workers’ cyber protection is not the same at home as it is in office. Although the effects of the virus are now subsiding, working remotely has embedded itself as the new normal. Thus, it is imperative for company management to take the necessary steps to ensure business continuity and be prepared to deal with an increased number of cyber threats. In our research, we provide a detailed classification for a group of tools which will facilitate risk mitigation and prevention. We also provide a selection of automated tools such as vulnerability scanners, monitoring and logging tools, and antivirus software. We outline each tool using tables, to show useful information such as advantages, disadvantages, scalability, cost, and other characteristics. Additionally, we implement decision trees for each category of tools, in an attempt to assist in navigating the large amount of information presented in this paper. Our objective is to provide a multifaceted taxonomy and analysis of mitigation tools, which will support companies in their endeavor to protect their computer networks. Our contribution can also help companies to have some type of cyber threat intelligence so as to put themselves one step ahead of cyber criminals.

scholarly journals A STATE OF ART AND PROSPECTS OF USED PNEUMATIC TIRES MANAGEMENT (REVIEW)

2021 ◽  
pp. 63-83
Author(s):  
I.O. Mikulionok
Keyword(s):  
Critical Analysis ◽  
Raw Materials ◽  
Chemical Processing ◽  
Detailed Classification ◽  
The World ◽  
Intended Use ◽  
State Of Art ◽  
Frag Ments ◽  
Pneumatic Tires

The basic data on the volume of production of pneumatic tires in the world and in Ukraine are presented. The need to improve the ways of handling pneumatic tires that have lost their con-sumer properties (worn out tires as a result of their intended use and tires rejected as a result of passing quality control during their manufacture) is shown as one of the most dangerous for the environment and promising in terms of using their properties. A detailed classification of methods for handling worn out and defective tires is proposed and a critical analysis of each of them is given. Particular attention is paid to the methods of utilization of tires, in particular, recycling, which makes it possible to efficiently use the secondary raw materials obtained from tires directly for their intended purpose. The features of physical, physicochemical and chemical processing methods, in particular combustion, gasification, pyrolysis of tires and their frag-ments, as well as the prospects for their decomposition under the influence of environmental factors, in particular microorganisms, are also considered. The main ways of solving the prob-lem of tires that have lost their consumer properties in Ukraine are proposed. Bibl. 88, Fig. 2.

scholarly journals Pattern Recognition by Hierarchical Feature Extraction

2003 ◽  
Vol 15 (3) ◽  
pp. 278-285
Author(s):  
Daigo Misaki ◽  
◽  
Shigeru Aomura ◽  
Noriyuki Aoyama
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Pattern Recognition ◽  
Feature Extraction ◽  
Input Data ◽  
Local Features ◽  
Detailed Classification

We discuss effective pattern recognition for contour images by hierarchical feature extraction. When pattern recognition is done for an unlimited object, it is effective to see the object in a perspective manner at the beginning and next to see in detail. General features are used for rough classification and local features are used for a more detailed classification. D-P matching is applied for classification of a typical contour image of individual class, which contains selected points called ""landmark""s, and rough classification is done. Features between these landmarks are analyzed and used as input data of neural networks for more detailed classification. We apply this to an illustrated referenced book of insects in which much information is classified hierarchically to verify the proposed method. By introducing landmarks, a neural network can be used effectively for pattern recognition of contour images.

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