ADVANCES IN GEOMETRY 是一本数学期刊，用于发表几何领域中质量卓越的原创研究文章。几何学是一个具有悠久传统和显着重要性的领域。空间和空间模式的研究是一项主要的数学活动；几何思想和几何语言渗透到所有的数学中。

Advances in Geometry is a mathematics journal dedicated to publishing high-quality original research articles in the field of geometry. Geometry, with its long-standing tradition and significant importance, involves the study of space and spatial patterns, which is a major mathematical activity. Geometric ideas and language permeate all areas of mathematics.

《Advances in Geometry》是一本专注于几何领域的数学期刊，致力于发表高质量的原创研究文章。几何学作为一个历史悠久且极具重要性的学科，涉及空间及其模式的研究，这是一项主要的数学活动。几何思想和语言在所有数学领域中都有着深刻的影响。

Advances in Geometry

Abstract Two subsets A , B of the plane are betweenness isomorphic if there is a bijection f : A → B such that, for every x , y , z ∈ A , the point f ( z ) lies on the line segment connecting f ( x ) and f ( y ) if and only if z lies on the line segment connecting x and y . In general, it is quite difficult to tell whether two given subsets of the plane are betweenness isomorphic. We concentrate on the case when each of the sets A , B is of the form C ∪ D where C is a circle and D is a finite set. We fully characterize the betweenness isomorphism classes in the family of all circles with three collinear points inside. In particular, we show that there are only countably many isomorphism classes, for which we provide an algebraic description.

Martin Doležal

Jan Kolář

Janusz Morawiec

Betweenness isomorphisms in the plane — the case of a circle and points

平面中的介数同构——圆与点的情形

Abstract The notion of a linear deformation of a codimension one foliation into contact structures was introduced in [5]. This concept is a special type of deformation of confoliations. In this paper, we study linear deformations of pairs of codimension one foliations into contact pairs. Applications of our main result are also provided.

Ameth Ndiaye

Aïssa Wade

Deformations of pairs of codimension one foliations

余一维叶状结构的变形对

Abstract In this paper, we introduce the notion of local quasi-isometry for metric germs and prove that two definable germs are quasi-isometric if and only if their tangent cones are bi-Lipschitz homeomorphic. Since bi-Lipschitz equivalence is a particular case of local quasi-isometric equivalence, we obtain Sampaio’s tangent cone theorem as a corollary. As an application, we provide a different proof of the theorem by Fernandes-Sampaio, which states that the tangent cone of a Lipschitz normally embedded germ is also Lipschitz normally embedded.

Nhan Nguyen

Local quasi-isometries and tangent cones of definable germs

局部拟等距与可定义芽的切锥

Abstract A p -set of equiangular lines in ℂ 3 is a set of p lines spanning ℂ 3 each pair of which has the same nonzero angle arccos c , where 0 &lt; c &lt; 1. It is known that via a real matrix representation, a pair of lines in ℝ 3 with angle arccos c yields a pair of isoclinic planes in ℝ 6 with angle arccos c . In this article we characterize all p -tuples of equi-isoclinic planes in ℝ 6 which come via our real matrix representation from p -tuples of equiangular lines in ℂ 3 . More precisely, we describe quadruples, quintuples up to nine-tuples of equiangular lines in ℂ 3 .

Boumediene Et-Taoui

Imène Lehbab

Abdenacer Makhlouf

Equiangular lines in ℂ<sup>3</sup>

ℂ<sup>3</sup>中的等角线

Abstract An isomorphism between two hermitian unitals is provided, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).

Abbreviation
Journal Impact	0.65
Quartiles(Global)	MATHEMATICS(Q3)

ISSN	1615-715X, 1615-7168
h-index	25

Publication Information	Publisher: Walter de Gruyter GmbH，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2001，Proportion of original research papers: 100.00%，Self Citation Rate:0.00%， Gold OA Rate: 4.80%
Average review cycle	网友分享经验：>12周，或约稿
Average recruitment ratio	网友分享经验：容易

Advances in Geometry

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Betweenness isomorphisms in the plane — the case of a circle and points

Deformations of pairs of codimension one foliations

Local quasi-isometries and tangent cones of definable germs

Equiangular lines in ℂ³

An isomorphism between unitals and between related classical groups

Betweenness isomorphisms in the plane — the case of a circle and points

Deformations of pairs of codimension one foliations

Local quasi-isometries and tangent cones of definable germs

Equiangular lines in ℂ³

An isomorphism between unitals and between related classical groups

Advances in Geometry

Journal Citation Format

A journal article with 1 author

A journal article with 2 authors

A journal article with 3 authors

A journal article with 5 or more authors

Books Citation Format

Thesis Citation Format

Web sites Citation Format

Patent Citation Format

Staying up late manually editing references? ivySCI automatically matches journals and helps you generate references with a single click.

Share Submission Experience

Betweenness isomorphisms in the plane — the case of a circle and points

Deformations of pairs of codimension one foliations

Local quasi-isometries and tangent cones of definable germs

Equiangular lines in ℂ3

An isomorphism between unitals and between related classical groups

Betweenness isomorphisms in the plane — the case of a circle and points

Deformations of pairs of codimension one foliations

Local quasi-isometries and tangent cones of definable germs

Equiangular lines in ℂ3

An isomorphism between unitals and between related classical groups

Equiangular lines in ℂ³

Equiangular lines in ℂ³