Metric kinematic planes and their representation by ν-local systems

Helmut Karzel; Kay Sörensen

doi:10.1007/s00022-011-0075-1

Metric kinematic planes and their representation by ν-local systems

Helmut Karzel
, Kay Sörensen

Department of Mathematics

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

Abstract

Planes with a regularly operating commutative group and with reflections on the lines through a distinguished point o, such that the 3-reflection theorem is valid for any three lines through o, are characterized algebraically as subplanes of locally euclidean planes. A slight weakening of the conditions yields to locally pseudo euclidean planes.

Original language	English
Pages (from-to)	85-103
Number of pages	19
Journal	Journal of Geometry
Volume	100
Issue number	1-2
DOIs	https://doi.org/10.1007/s00022-011-0075-1
State	Published - Apr 2011

Keywords

(locally) (pseudo) Euclidean plane
(pseudo) Rectangular plane
Absolute plane
Kinematic algebra
Lotkerngeometrie
Metric ν-local algebra
ν-Local system

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10.1007/s00022-011-0075-1

Cite this

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abstract = "Planes with a regularly operating commutative group and with reflections on the lines through a distinguished point o, such that the 3-reflection theorem is valid for any three lines through o, are characterized algebraically as subplanes of locally euclidean planes. A slight weakening of the conditions yields to locally pseudo euclidean planes.",

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KW - (pseudo) Rectangular plane

KW - Absolute plane

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KW - Lotkerngeometrie

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KW - ν-Local system

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JO - Journal of Geometry

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Metric kinematic planes and their representation by ν-local systems

Abstract

Keywords

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