共查询到20条相似文献,搜索用时 15 毫秒
1.
Richard Koch 《Journal of Geometry》1993,47(1-2):77-85
Referring to articles of BELTRAMI (1865), DINI (1866) and CHARIAR (1978), but using a completely different approach, we determine allruled surfaces in Euclidean space 3, which are (at leastlocally) WEINGARTEN —-surfaces under theminimal assumption C2. Theskew ruled WEINGARTEN —surfaces can be characterized by havingconstant invariants d O (parameter of distribution), k (skewness of distribution) and (striction angle); theirfunctional (WEINGARTEN-)relation between the mean curvature H and the Gaussian curvature K of is of the form H= (-K)1/4 + (-K)3/4 with arbitrary real constants ,. These facts allow various geometric interpretations.
Herrn Prof. Dr. Oswald Giering zum 60. Geburtstag gewidmet 相似文献
Herrn Prof. Dr. Oswald Giering zum 60. Geburtstag gewidmet 相似文献
2.
H. Hagen 《Journal of Geometry》1983,21(1):157-163
In this paper we investigate (k+1)-dimensional generalized ruled surfaces generated by a one-parameter family of k-dimensional linear subspaces of the n-dimensional Euclidean space \(\mathbb{E}^n \) . 相似文献
3.
Friedrich Manhart 《Journal of Geometry》2000,69(1-2):166-171
If the (euclidean) Gauss curvature of a surface in 3-space is nowhere vanishing, we have a uniqueaffine normal in every point of the surface and the set of affine normals forms a line congruence. According to the euclidean situation one can discuss existence and degeneration ofaffine focal surfaces. A cylinder of revolution in euclidean space can be characterized by the property, that all normals intersecttwo straight lines. The corresponding property in affine geometry leads to certainaffine surfaces of revolution, whose meridian curves (plane sections through a fixed axis) can be determined. If we assume the affine focal surfaces to coincide (the affine Weingarten endomorphism has double eigenvalues in every point) and degenerate intoone straight line, then the surface is aruled surface the generators of which areparallel to a plane.
Herrn Professor Dr. Gerhard Geise zum 70. Geburtstag gewidmet 相似文献
Herrn Professor Dr. Gerhard Geise zum 70. Geburtstag gewidmet 相似文献
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5.
Ludwig Bieberbach 《Annali di Matematica Pura ed Applicata》1961,55(1):273-295
Zusammenfassung Jede sich ins Unendliche erstreckende dreimal stetig differenzierbare konvexe Rotationsfl?che kann mit einem Tschebychefnetz
bedeckt werden. Bei beschr?nkten Rotationseifl?chen ist eine solche Bedeckung erst m?glich, wenn sie durch zwei zu einander
senkrechte kurze Meridianb?gen durch einen bestimmten ihrer beiden Nabelpunkte berandet worden ist.
Enrico Bompiani zu seinem wissenschaftlichen Jubil?um. 相似文献
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7.
Martin Barner 《Mathematische Zeitschrift》1955,62(1):50-93
Ohne ZusammenfassungHerrnWilhelm Süss zum 60. Geburtstag am 7. März 1955 gewidmet.HerrnG. Bol habe ich für sein großes Interesse an den vorliegenden Untersuchungen zu danken Verschiedene Zusammenhänge und Ergebnisse gehen auf ihn zurück. Weitere Ergebnisse finden sich in seiner Projektiven Differentialgeometrie, Teil 3 (im Erscheinen).Über die Grundgedanken dieser Arbeit habe ieh auf der Tagung der Deutschen Mathematikervereinigung in München 1952 berichtet. 相似文献
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Karl Strubecker 《Archiv der Mathematik》1954,5(1-3):32-38
Ohne ZusammenfassungHerrn Professor Dr.Alexander Ostrowski zum 60. Geburtstag am 25. 9. 1953 gewidmet 相似文献
10.
Karlheinz Schüffler 《manuscripta mathematica》1979,30(2):163-197
Multiply connected minimal surfaces of genus 0 with only simple interior branch points, for which the corresponding boundary value problem $$\Delta h - K|x_z |^2 h = 0; h_{|\partial \Omega } = 0$$ (K is the Gauss curvature and xz is the complex gradient of the surface x) is uniquely solvable and which have the property, that the condition K|xz|2≠0 holds in the branch points, are always isolated and stable solutions of the Plateau problem, corresponding to their boundary curves. To achieve these results one has to consider the conformal type as a variable. We give a method to perform the variation of the conformal type for holomorphic functions. Using the Weierstrass representation we thus obtain a differentiable structure on the set of multiply connected minimal surfaces. We find interesting connections between the classical Riemann-Hilbert problem and Fredholm properties of a projection operator on this manifold. 相似文献
11.
Walter Wunderlich 《Archiv der Mathematik》1963,14(1):204-211
Ohne ZusammenfassungProf.Hermann Schmidt zum 60. Geburtstag 相似文献
12.
Walter Wunderlich 《Monatshefte für Mathematik》1961,65(3):291-300
Ohne ZusammenfassungProf. E. Kruppa zum 75. GeburtstagMit 3 Textabbildungen 相似文献
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H. Brauner 《Monatshefte für Mathematik》1962,66(2):105-109
Ohne ZusammenfassungHerrn Prof. Dr. Paul Funk zum 75. Geburtstag gewidmet 相似文献
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Wendelin Degen 《manuscripta mathematica》1986,55(1):9-38
A surface in projective space generated by a one parameter family of conics is called a conic surface of Blutel if the tangent planes of taken along a generating conic, envelop a quadratic cone. If the conjugate curves (with respect to the generating conics) are conics, too, we call a two-fold Blutel's conic surface. In an earlier paper [4] it was shown that the planes of both conic families, the generating and the conjugate one, belong to a pencil, each. The present paper completes these investigations by integrating the derivative equations (3), (8), (9), (10). As a final result, a complete classification of all these surfaces is given. They are all algebraic of at most fourth order and furthermore—besides the quadrics and certain degenerate cases—they are complex projectively equivalent to the cyclides of Dupin. 相似文献
18.
Heinz-Otto Kreiss 《Annali di Matematica Pura ed Applicata》1956,41(1):105-111
Sunto Superficie sizigetiche di S
3
sono quelle d'ordine2n con singolarità in un dato gruppo di n
3
punti, intersezione completa di 3 superficie d'ordine n. Per mezzo di metodi iperspaziali e con una scelta opportuna della
rete di superficie d'ordine n si perviene alla costruzione di esempi di superficie d'ordine2n con3n
3
—2n
2
singolarità isolate per n≤7 e per lo meno con 5/2n3−3/2n2 singolarità per n qualsiasi.
相似文献
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Stylianos Stamatakis 《manuscripta mathematica》1991,71(1):29-33
Let ℱ: x=x(u1, u2) be a C3-surface in the euclidean space E3, n the unit normal vector of ℱ and let
. We consider the vector
of ℝ6 and we denote with μ the rank of the matrix (a, a1, a2, a1, 1, a1, 2, a2, 2). We then prove the Theorem: ℱ is a W-surface if and only if μ≦5. Further, μ is 4 resp. 3 if and only if the surface ℱ is
part of a cylinder of revolution resp. part of a sphere or a plane.
相似文献