Hyperplanes and motions of dimension-free hyperbolic geometry

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Erscheinungsjahr:
2009
Medientyp:
Text
Schlagworte:
  • Coordinates
  • Dimension-free
  • Hyperbolic geometry
  • Hyperbolic hyperplanes
  • Hyperbolic translations
Beschreibung:
  • In Section 1 we characterize hyperbolic hyperplanes of dimension-free hyperbolic geometry over the real inner product space X of arbitrary (finite or infinite) dimension greater than 1 by euclidean hyperplanes ∋ 0 of X ⊕ ℝ intersecting the surface {(x,√1 + x2) {pipe} x ∈ X}. This is for X = ℝ2 a well-known result of the classical theory, since the Weierstraβ model of plane hyperbolic geometry defines hyperbolic lines via the euclidean planes of ℝ3 through 0 intersecting the surface in question. - In Section 2 formulas will be derived representing dimension-free hyperbolic motions of X as well as products consisting of two such factors. - Finally, in Section 3, coordinates will be considered describing naturally the action of hyperbolic translations on points. © 2009 Birkhäuser Verlag Basel/Switzerland.
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  • info:eu-repo/semantics/closedAccess
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/6a358e59-109d-4f47-93c8-073047f11660