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  • 1990-1994  (5)
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Material
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Transnormality and the infinitesimal rectangle property (1990)
    Springer
    Journal of geometry 37 (1990), S. 181-190 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230371
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A cyclographic approach to the vertices of plane curves (1994)
    Springer
    Journal of geometry 50 (1994), S. 186-201 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a closed plane curveα the centers of distance functions are considered satisfying the condition that the function attains at least two absolute minima alongα. From the topology of the closure of this set some information on specific vertices of the curve can be obtained. If a simply closed curveα has a finite number of vertices only, then the structure of this set is given by a tree, composed from regular arcs, such that the end points of this tree belong to minimal osculating circles ofα, which entirely are located in the interior ofα. Furthermore, the curve can be reconstructed from this set as the envelope of a suitable family of circles. These relations are used to give alternative proofs and extensions of several known vertex theorems for closed curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222675
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Self-parallel and transnormal curves (1991)
    Springer
    Geometriae dedicata 38 (1991), S. 175-191 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The construction of examples of self-parallel curves from a closed central curve given by F. J. Craveiro de Carvalho and S. A. Robertson is extended to general closed regular curves without the assumption of non-vanishing curvature made there. Furthermore, every self-parallel curve in 3-space is shown to be of the type obtained by this construction, if the order of the self-parallel group is greater than 2. These considerations are used to present examples for transnormal curves in 4-space with arbitrarily high degree of transnormality, disproving a long-standing conjecture of M. C. Irwin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181217
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Comment on ‘Euclidean hypersurfaces with reflection properties’ (1991)
    Springer
    Geometriae dedicata 39 (1991), S. 357-359 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00150761
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    On the rectangle property for plane continua and immersed topological hypersurfaces (1990)
    Springer
    Geometriae dedicata 33 (1990), S. 163-176 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A subset of Euclidean space is said to satisfy the rectangle property if no rectangle has exactly three vertices in this subset. According to Besicovitch and Dnazer, circles are characterized by this property among convex curves. Here, more general characterizations of this type are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00183082
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    Paper (German National Licenses)
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