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  • 1
    Electronic Resource
    Electronic Resource
    New Construction for Spherical Minimal Immersions (1997)
    Springer
    Geometriae dedicata 67 (1997), S. 187-196 
    Details
    ISSN: 1572-9168
    Keywords: Spherical minimal immersion ; harmonic projection operator.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe a general method of manufacturing new minimal immersions between round spheres out of old ones. The resulting spherical minimal immersions are given analytically in terms of the harmonic projection operator and have higher source dimensions. Applied to classical examples, this gives an abundance of new minimal immersions of even-dimensional spheres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004900218939
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  • 2
    Electronic Resource
    Electronic Resource
    Quadratic eigenmaps between spheres (1995)
    Springer
    Geometriae dedicata 56 (1995), S. 35-52 
    Details
    ISSN: 1572-9168
    Keywords: 54-xx
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A quadratic formf:S m →S n between spheres is separable if, up to isometries on the source and the range, the components off are pure or mixed quadratic polynomials. The space parametrizing the separated quadratic eigenmapsf is shown here to fiber over a semi-algebraic set with each fiber a finite-dimensional compact convex body. Form = 3, this gives a new description of the parameter space of all quadratic eigenmapsf:S 3 →S m as a fibration over an ‘inflated tetrahedron’ and generic hexagonal fibres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01263612
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  • 3
    Electronic Resource
    Electronic Resource
    Construction Des Applications Harmoniques Non Rigides D'un Tore Dans La Sphère (1983)
    Springer
    Annals of global analysis and geometry 1 (1983), S. 105-118 
    Details
    ISSN: 1572-9060
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Zusammenfassung Le but de Particle present est l'étude des déformations harmoniques géodésiques. f d'un tore dans la sphere avec la densité d'énergie 1/2 . Nous montrons que tout les deformations harmoniques sont isométriques, c'est-à-dire que l'application f est rigide, si et seulement si f est totalement géodésique. De plus nous calculons les espaces de deformations harmoniques pour la 3-sphère.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02330008
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  • 4
    Electronic Resource
    Electronic Resource
    Constructions of harmonic polynomial maps between spheres (1994)
    Springer
    Geometriae dedicata 50 (1994), S. 57-79 
    Details
    ISSN: 1572-9168
    Keywords: 58E20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The complexity of λ q -eigenmaps, i.e. homogeneous degreeq harmonic polynomial mapsf:S m →S n, increases fast with the degreeq and the source dimensionm. Here we introduce a variety of methods of manufacturing new eigenmaps out of old ones. They include degree and source dimension raising operators. As a byproduct, we get estimates on the possible range dimensions of full eigenmaps and obtain a geometric insight of the harmonic product of λ2-eigenmaps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01263652
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  • 5
    Electronic Resource
    Electronic Resource
    Covering of the plane by discs (1984)
    Springer
    Geometriae dedicata 16 (1984), S. 315-333 
    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/BF00147874
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  • 6
    Electronic Resource
    Electronic Resource
    On classification of orthogonal multiplications à la do carmo-wallach (1987)
    Springer
    Geometriae dedicata 22 (1987), S. 251-254 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The space of range-equivalence classes of full orthogonal multiplications F: ℝ n ×ℝ n →ℝ p , n≤p ≤n 2, is shown to be a compact convex body lying in so(n)⊗so(n). Furthermore, the dimension of the space of equivalence classes is determined to be (n 2(n−1)2)/4−n(n−1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181271
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  • 7
    Electronic Resource
    Electronic Resource
    On transversal infinitesimal automorphisms for harmonic foliations (1987)
    Springer
    Geometriae dedicata 24 (1987), S. 229-236 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider a harmonic Riemannian foliation ℱ, and study the transversal infinitesimal automorphisms of ℱ with certain additional properties like being transversal conformal or Killing (= metric). Such automorphisms (modulo Killing automorphisms) are related to the stability of ℱ. A special study is made for the case of a foliation with constant transversal scalar curvature, and more particularly with transversal Ricci curvature proportional to the transversal metric (Einstein foliation).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00150938
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  • 8
    Electronic Resource
    Electronic Resource
    Synthesis of benzopyran derivatives, XV Preparation of arylsulfonyloxy-2,2-dimethyl-2H-chromenes (1990)
    Springer
    Monatshefte für Chemie 121 (1990), S. 403-411 
    Details
    ISSN: 1434-4475
    Keywords: 2,2-Dimethyl-4-chromanones ; Reduction with NaBH4 ; 2,2-Dimethyl-4-hydroxychromans ; Dehydration ; Conformational analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Reduktion von Arylsulfonyloxy-2,2-dimethyl-4-chromanonen (6–15) und anschließende Dehydratisierung liefert Arylsulfonyloxy-2,2-dimethyl-2H-chromene (26–35).
    Notes: Summary Arylsulfonyloxy-2,2-dimethyl-2H-chromenes (26–35) have been synthesized by reduction of arylsulfonyloxy-2,2-dimethyl-4-chromanones (6–15) followed by dehydration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00809457
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  • 9
    Electronic Resource
    Electronic Resource
    1,3-Dipolare Cycloadditionen von 3,4-Dihydro-6,7-dimethoxyisochinolinium-N-methoxycarbonylmethylid mit N-substituierten Maleinimiden (1990)
    Springer
    Monatshefte für Chemie 121 (1990), S. 529-537 
    Details
    ISSN: 1434-4475
    Keywords: Pyrrolo[2,1-a]isoquinolines ; Azomethine ylides ; NMR ; Stereochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary 1,3-Dipolar cycloadditions of 3,4-dihydro-6,7-dimethoxyisoquinolinium-N-methoxycarbonylmethylide2 with N-phenyl- and N-methylmaleimide (3 and4) have been investigated. Cycloadducts of theendo- andexo-type were formed, the structure elucidation and conformational analysis of which has been performed by NMR methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00810862
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  • 10
    Electronic Resource
    Electronic Resource
    The Bogoliubov inner product in quantum statistics (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 205-216 
    Details
    ISSN: 1573-0530
    Keywords: 82B10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A natural Riemannian geometry is defined on the state space of a finite quantum system by means of the Bogoliubov scalar product which is infinitesimally induced by the (nonsymmetric) relative entropy functional. The basic geometrical quantities, including sectional curvatures, are computed for a two-level quantum system. It is found that the real density matrices form a totally geodesic submanifold and the von Neumann entropy is a monotone function of the scalar curvature. Furthermore, we establish information inequalities extending the Cramér-Rao inequality of classical statistics. These are based on a very general new form of the logarithmic derivative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739578
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