Eighteen Essays in Non-Euclidean Geometry最新文献_第2页

Area and volume in non-Euclidean geometry 非欧几里得几何中的面积和体积

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2019-03-31 DOI: 10.4171/196-1/11

N. Abrosimov, A. Mednykh

引用次数: 3

The Gauss–Bonnet theorem and the geometry of surfaces 高斯-邦尼特定理与曲面几何

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2019-03-31 DOI: 10.4171/196-1/8

Son Lam Ho

引用次数: 0

Hermitian trigonometry 埃尔米特三角

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2019-03-31 DOI: 10.4171/196-1/17

B. Et-Taoui

引用次数: 0

On a theorem of Lambert: medians in spherical and hyperbolic geometries 关于朗伯定理:球面和双曲几何中的中值

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2019-03-31 DOI: 10.4171/196-1/4

Himalaya Senapati

引用次数: 0

A theorem on equiareal triangles with a fixed base 关于底边固定的等边三角形的定理

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2019-02-27 DOI: 10.4171/196-1/18

V. Pambuccian

引用次数: 0

Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry 欧几里得几何和非欧几里得几何中框架的静力学和运动学

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2017-07-07 DOI: 10.4171/196-1/12

Ivan Izmestiev

引用次数: 10

Spherical and hyperbolic conics 球面和双曲二次曲线

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2017-02-22 DOI: 10.4171/196-1/15

Ivan Izmestiev

引用次数: 9

Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions 球面、双曲和其他射影几何:凸性、对偶性、过渡

Eighteen Essays in Non-Euclidean Geometry Pub Date : 2016-11-03 DOI: 10.4171/196-1/16

Franccois Fillastre, Andrea Seppi

{"title":"Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions","authors":"Franccois Fillastre, Andrea Seppi","doi":"10.4171/196-1/16","DOIUrl":"https://doi.org/10.4171/196-1/16","url":null,"abstract":"Since the end of the 19th century, and after the works of F. Klein and H. Poincar'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen as a \"limit\" of both geometries. Then all the geometries that can be obtained in this way. Some of these geometries had a rich development, most remarkably hyperbolic geometry and the Lorentzian geometries of Minkowski, de Sitter and anti-de Sitter spaces, which in higher dimension have had large interest for a long time in mathematical physics and more precisely in General Relativity. Moreover, some degenerate spaces appear naturally in the picture, namely the co-Euclidean space (the space of hyperplanes of the Euclidean space), and the co-Minkowski space (that we will restrict to the space of space-like hyperplanes of Minkowski space), first because of duality reasons, and second because they appear as limits of degeneration of classical spaces. In fact, co-Minkowski space recently regained interest under the name half-pipe geometry. The purpose of the present paper is to provide a survey on the properties of these spaces, especially in dimensions 2 and 3, from the point of view of projective geometry. Even with this perspective, the paper does not aim to be an exhaustive treatment. Instead it is focused on the aspects which concern convex subsets and their duality, degeneration of geometries and some properties of surfaces in three-dimensional spaces. The presentation is intended to be elementary, hence containing no deep proofs of theorems, but trying to proceed by accessible observations and elementary proofs.","PeriodicalId":429025,"journal":{"name":"Eighteen Essays in Non-Euclidean Geometry","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115720435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 29