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  • 1
    Electronic Resource
    Electronic Resource
    Zur Möbiusgeometrie der Flächenstreifen (1973)
    Springer
    Monatshefte für Mathematik 77 (1973), S. 416-432 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01295320
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Zur Möbiusgeometrie der Berührkreisscharen (1975)
    Springer
    Monatshefte für Mathematik 80 (1975), S. 307-318 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Making use of an earlier result of the theory of stripes in three-dimensional conformal spaceM 3 we obtain a moving frame and derivational formulas for one-parameter families of tangent circles inM 3. Avoiding invariant parameters we can set up a bijection of the tangent circles into the osculating circles that preserves the duple ratio. The following section deals with loxodromes on Dupin cyclides. Finally with the aid of a modified stereographic projection we show how to get the Frenet formulas of the euclidian theory of spacecurves from the derivational formulas for tangent circles inM 3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01472578
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  • 3
    Electronic Resource
    Electronic Resource
    Zur Möbiusgeometrie der Kurventheorie (1976)
    Springer
    Monatshefte für Mathematik 81 (1976), S. 141-148 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using the derivational formulas for stripes we derive in section 1 the derivational formulas for spacecurves in three-dimensional conformal spaceM 3. With a curve we associate locally a one-parameter family of so calledQ 4-surfaces having contact of order 5. AQ 4-surface is generated by two special parabolic pencils of spheres. We investigate alsoQ 4-surfaces having contact of orderk(k=7,8). Section 2 deals with isogonal-trajectories on the surface of the principal circles of the given spacecurve. We avoid invariant parameters as used in projective geometry for getting results of conformal geometry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01301238
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