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  • 1
    Digitale Medien
    Digitale Medien
    Transnormale Isotopien und transnormale Kurven (1971)
    Springer
    Manuscripta mathematica 4 (1971), S. 361-372 
    Details
    ISSN: 1432-1785
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For transnormal manifolds which admit a nontrivial decktransformation leaving the transnormal frames invariant there is a natural construction of “parallel” transnormal manifolds. Generalizing a result of M. C. IRWIN [3] this construction is applied to show that every transnormal embedding of a 1-sphere is isotopic through transnormal embeddings to a spherical embedding. Moreover we show that the transnormal frame of a transnormal curve has only a finite number of points.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01168703
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  • 2
    Digitale Medien
    Digitale Medien
    Krümmungseigenschaften transnormaler Mannigfaltigkeiten (1970)
    Springer
    Manuscripta mathematica 3 (1970), S. 375-390 
    Details
    ISSN: 1432-1785
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In [6] ROBERTSON introduced the notion of a transnormal manifold as a generalization of a compact connected closed hypersurface of constant width in Euclidean space. This paper includes a detailed proof of the fact that the projection of a transnormal manifold on its space of normal planes is a covering map. Furthermore we prove the following generalization of a property of closed convex hypersurfaces of constant width: If two points p, q of a transnormal manifold have the same normal plane, then (for a suitable choice) the sum of the corresponding radii of principal curvature in direction of the common normal line is equal to the distance of p and q. Finally there are given examples of transnormal manifolds, which do not possess minimal total absolute curvature.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01168293
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  • 3
    Digitale Medien
    Digitale Medien
    Decktransformationen transnormaler Mannigfaltigkeiten (1971)
    Springer
    Manuscripta mathematica 4 (1971), S. 179-199 
    Details
    ISSN: 1432-1785
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For every transnormal m-manifold V (see [3] or [7]) in ℝn ν:V→W, mapping pεV into its normal plane ν(p) is a covering map onto a submanifold W of the open Grassmannian Hn,n−m of all (n−m)-dimensional planes in ℝn. The transnormal frame T:=ν−1(ν(p)) admits a transitive operation by a group J of isometries. The group action of the covering transformations of (V,ν,W) on T commutes with the action of J. The elements of J, which are restrictions of covering transformations to T, are exactly the elements of the centre of J. This property is applied to show the existence of nontrivial covering transformations of (V,ν,W) for n−m≦3.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169411
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  • 4
    Digitale Medien
    Digitale Medien
    EMIS 2000: The European Mathematical Information Service and its developments (2001)
    Bradford : Emerald
    Online information review 25 (2001), S. 165-172 
    Details
    ISSN: 1468-4527
    Quelle: Emerald Fulltext Archive Database 1994-2005
    Thema: Buch- und Bibliothekswesen, Informationswissenschaft
    Notizen: The European Mathematical Information Service (EMIS) is a cooperative venture between several international partners under the umbrella of the European Mathematical Society (EMS). The main purpose of EMIS is to provide access to freely available information on mathematics in the Web. As an important part of EMIS an electronic library is stored on the main server and its mirrors, collecting all freely accessible electronic journals in mathematics combined with electronic versions of printed journals. It also contains electronic proceedings, volumes and monographs. This core content is embedded in, and linked with, an environment of comprehensive facilities for accessing mathematical research papers: literature information databases, projects for one-stop shopping sites for mathematics on the Web, freely available digital content of classical mathematical publications and access to electronic grey literature. The aim of this article is to describe this part of EMIS in some detail.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1108/14684520110395290
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  • 5
    Digitale Medien
    Digitale Medien
    Projections of transnormal manifolds (1989)
    Springer
    Journal of geometry 36 (1989), S. 183-187 
    Details
    ISSN: 1420-8997
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Transnormal manifolds are generalizations of convex hypersurfaces of constant width (see [7]). For such hypersurfaces it is known that every orthogonal projection onto a hyperplane has an outline which is of constant width, too. Orthogonal projections of transnormal manifolds have been studied by F.J. Craveiro de Carvalho [1] in the case when the projection is an immersion onto a convex hypersurface of constant width in a suitable affine subspace of the ambient Euclidean space. Here it will be shown that transnormality is not preserved under orthogonal projection onto hyperplanes without assuming that the manifold has the topological type of a sphere. This implies another general version of the transnormal graph theorem (see [2]). Furthermore, in the case of closed transnormal curves in 3-space also non-orthogonal parallel projection onto planes cannot preserve transnormality as is shown in the last section.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01231032
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  • 6
    Digitale Medien
    Digitale Medien
    Transnormality and the infinitesimal rectangle property (1990)
    Springer
    Journal of geometry 37 (1990), S. 181-190 
    Details
    ISSN: 1420-8997
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01230371
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  • 7
    Digitale Medien
    Digitale Medien
    Eine Bemerkung zur Integralformelmethode (1972)
    Springer
    Archiv der Mathematik 23 (1972), S. 324-328 
    Details
    ISSN: 1420-8938
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01304889
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  • 8
    Digitale Medien
    Digitale Medien
    Comment on ‘a remark on totally vicious space-time’ (1989)
    Springer
    Journal of geometry 36 (1989), S. 188-188 
    Details
    ISSN: 1420-8997
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01231033
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  • 9
    Digitale Medien
    Digitale Medien
    Constant width and transnormality in spheres (1996)
    Springer
    Journal of geometry 56 (1996), S. 25-33 
    Details
    ISSN: 1420-8997
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The aim of this note is to investigate the behaviour of exterior and interior parallels at distanceε to a given convex body of constant width in the unitn-sphere. The boundaries of these bodies are 2-transnormal topological (n−1)-spheres. The range ofε is determined where these transnormal topological (n−1)-spheres bound convex bodies of constant width as well. In particular this leads to the following main result: LetC be a body of constant width (π/2)+x ε ((π/2), π) in the unit sphere Sn. ThenC contains a body C of constant width (π/2)−x such thatC is the closedx-neighborhood of C. Moreover, the bodyC is smooth.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01222680
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  • 10
    Digitale Medien
    Digitale Medien
    Wackelige Gelenkwerke und wackelige Polyeder in Der sphärischen Geometrie (1985)
    Springer
    Journal of geometry 25 (1985), S. 39-48 
    Details
    ISSN: 1420-8997
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Infinitesimal rigidity and shakiness of jointed rodworks or polyhedra have been of major interest in recent research in geometry. In this paper structures of this type are investigated in spheres and projective spaces. A transformation is given showing that essentially no new structures occur in these spaces compared with the euclidean case. The main tool is the projective invariance of shaky structures. Shaky structures in euclidean space can be obtained as affine sections of shaky structures in a projective space of the same dimension.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01222944
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