The geometry of hyperbolic lines in polar spaces

نویسنده

  • Hans Cuypers
چکیده

In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric characterizations of these and related spaces. These results can be viewed as the geometric counterpart of the theory of k-transvection groups as developed by Timmesfeld and others.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Metric and periodic lines in the Poincare ball model of hyperbolic geometry

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.

متن کامل

An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach

‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing with the Lorentz group and its ‎underlying hyperbolic geometry‎. ‎They defined the Chen addition and then Chen model of hyperbolic geomet...

متن کامل

The generating rank of the symplectic grassmannians: Hyperbolic and isotropic geometry

Exploiting the interplay between hyperbolic and isotropic geometry, we prove that the grassmannian of totally isotropic k-spaces of the polar space associated to the symplectic group Sp2n(F) has generating rank ( 2n k ) − ( 2n k−2 ) when Char(F) = 2. c © 2006 Elsevier Ltd. All rights reserved.

متن کامل

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

متن کامل

On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009