منابع مشابه
The Conformal Geometry of Billiards
This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an SL2R action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of “optimal” billiard tables, those with the simplest trajectory structure.
متن کاملÁNOS P ALLAGI , B ENEDEK S CHULTZ , J ENÖ S ZIRMAI On Regular Square Prism Tilings in S̃L 2 R Space On Regular Square Prism
The SL2R Lie-group consists of the real 2× 2 matrices ( d b c a ) with unit determinant ad − cb = 1. The S̃L2R geometry is the universal covering group of this group, and is a Lie-group itself. Because of the 3 independent coordinates, S̃L2R is a 3-dimensional manifold, with its usual neighbourhood topology. In order to model the above structure on the projective sphere PS3 and space P3 we introd...
متن کاملActions of R · S̃L 2 R on Laguerre planes related to the Moulton planes ∗
We construct flat Laguerre planes that admit the universal covering group of SL2R, extended by a factor R, as a group of automorphisms. These planes contain the affine Moulton planes as derived planes, and they are constructed by gluing together two copies of a Moulton plane, folded up along their fixed lines. The action of the Moulton group carries over (modulo Z2) to the Laguerre planes, and ...
متن کاملSixteen-dimensional Locally Compact Translation Planes Admitting Sl2 H as a Group of Collineations
In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...
متن کاملبررسی رویه های مینیمال انتقالی در 3-منیفلد sol3
در این پایان نامه هندسه های سه بعدی تورستون که عبارتند از e3;h3; s3;h2 * r; s2 * r;^sl2r;nil3; sol3 مورد بررسی قرار گرفته و در نهایت با انگاره ی هندسی تورستون آشنا خواهیم شد. در ادامه 3-منیفلد همگن sol3 را بیشتر مورد بررسی قرار داده و به محاسبه رویه های مینیمال انتقالی در این فضا پرداخته و آنها را در سه گروه دسته بندی خواهیم کرد
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1986
ISSN: 0001-8708
DOI: 10.1016/0001-8708(86)90078-2