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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Behavior of geodesics, and tilings of hyperbolic space

Behavior of geodesics, and tilings of hyperbolic space

Balkan, Vladimir

Paperback

Geometry

ISBN10: 6208446678
ISBN13: 9786208446673
Publisher: LAP Lambert Academic Publishing
Published: Aug 9 2025
Pages: 112
Weight: 0.35
Height: 0.27 Width: 6.00 Depth: 9.00
Language: English
The presented work is a research in the field of the geometry of two-dimensional hyperbolic (equipped with a metric of constant negative curvature) manifolds and studies tilings in hyperbolic n-space of arbitrary dimension by polytopes. In part one we introduce a new method (method of colour multilaterals) to describe the global behavior of geodesics on a arbitrary hyperbolic manifolds of dimension two. The best behaved tilings are the face-to-face tilings by convex polytopes. Of a special interest are tilings in hyperbolic n-space. In part two the main results of this publication are obtained for tilings (isohedral, non-isohedral, face-to-face, non- face-to-face) in the hyperbolic n-space of arbitrary dimension for any, () by compact and non-compact polytopes and we describe their discrete isometry groups and properties. Torsion free groups are especially important.

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