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On certain loci projectivly connected with a given plane curve ... /Harding, Arthur M. January 1900 (has links)
Thesis (PH. D)--University of Chicago, 1916. / "Private edition, distributed by the University of Chicago Libraries, Chicago, Illinois." "Reprinted from Giornale di matematiche di Battaglini Vol. LIV, 1916." Includes bibliographical references. Also available on the Internet. Also issued online.
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Pairs of surfaces in five-dimensional space ...Wilcox, L. R. January 1938 (has links)
Thesis (Ph. D.)--University of Chicago, 1935. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."
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Recherches sur la géométrie projective réglée différentielleRozel, Octave. January 1935 (has links)
Thesis--Université de Liege. / "Extrait des Mémoires de la Société royale des sciences de Liége, 3e série, tome 20."
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Projective differentiaalmeetkunde der analytische regeloppervlakken in R₄ ...Bos, Wilhelmus Johannes. January 1942 (has links)
Proefschrift--Amsterdam. / "Stellingen": [2] p. inserted.
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Recherches sur la géométrie projective réglée différentielleRozel, Octave. January 1935 (has links)
Thesis--Université de Liege. / "Extrait des Mémoires de la Société royale des sciences de Liége, 3e série, tome 20."
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On certain loci projectivly connected with a given plane curve ...Harding, Arthur M. January 1900 (has links)
Thesis (PH. D)--University of Chicago, 1916. / "Private edition, distributed by the University of Chicago Libraries, Chicago, Illinois." "Reprinted from Giornale di matematiche di Battaglini Vol. LIV, 1916." Includes bibliographical references.
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Relations between the metric and projective theories of space curves ... /Simpson, Thomas McNider, January 1920 (has links)
Thesis (Ph. D.)--University of Chicago, Department of Mathematics, 1917. / "Private edition, distributed by the University of Chicago Libraries." Includes bibliographical references. Also available on the Internet.
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Contributions to the theory of conjugate nets ...Davis, Watson M., January 1935 (has links)
Thesis (Ph. D.)--University of Chicago, 1933. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."
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Conjugate systems characterized by special properties of their ray congruences ...Olson, Emma Julia, January 1934 (has links)
Thesis (Ph. D.)--University of Chicago, 1932. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Bibliography: p. 55-56.
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Flecnodal and LIE-curves of ruled surfaces / Fleknodal- und LIE-Kurven von RegelflächenKhattab, Ashraf 09 November 2005 (has links) (PDF)
If we consider ruled surfaces of the projective 3-space as a one parameter family of lines, then they appear in the well-known KLEIN-model of lines in the projective 3-space as curves of a hyperquadric in the projective 5-space. The osculating spaces of such a curve are represented in the projective 3-space by spaces of linear complexes. Those points of a generator e of the ruled surface, in which the tangent bundles are in the same time complex line bundles in the accompanying osculating line complex of the ruled surface along e, are called the LIE-points of e. The LIE-points fulfil two (real or imaginary conjugate) curves on the ruled surface called the LIE-curves. The support of the osculating-3-space of the ruled surface along a regular non-torsal generator e are two, one or zero straight lines in the osculating regulus. If thes straight lines exist, one calls them the flecnode tangents of the ruled surface. On a hyperbolic ruled surface build the points of contact of the flecnode tangents two projective distinguished curves called the flecnode curves. In this work we present the different methods of treating these curves in the history, and we give a new explicit calculation of the flecnode points and the LIE-points depending on the basis of a PLÜCKER-coordinates representation of the ruled surface. In addition we study the questions that appears by considering the LIE-curves of a ruled surface to form a pair of BERTRAND curves for which this ruled surface is the surface of common main normals. For example, the question about ruled surfaces, whose LIE-curves are orthogonal to the generators will be answered here. / Regelflächen des projektiven 3-Raums erscheinen, als (eindimensionalen) Geradenmengen aufgefasst, im bekannten KLEINschen Punktmodell der Geradenmenge vom projektiven 3-Raum als Kurven einer Hyperquadrik in einem projektiven 5-Raum. Die Schmiegräume einer solchen Kurve werden im projektiven 3-Raum durch Räume linearer Komplexe repräsentiert. Diejenigen Punkte einer Erzeugende e der Regelfläche, in denen die Tangentenbüschel gleichzeitig auch Komplexgeradenbüschel im begleitenden Schmiegkomplex von e sind, heißen LIE-Punkte von e. Die LIE-Punkte erfüllen zwei (reelle oder konjugiert imaginäre) Kurvenzüge auf der Regelfläche, die LIE-Kurven. Die Träger des Schmieg-3-Raums der Regelfläche längs einer reguläre nichttorsalen Erzeugende e sind zwei, eine oder null Geraden im Schmiegregulus. Sofern diese Geraden existieren, nennt man sie die Fleknodaltangenten der Regelfläche. Auf hyperbolischen Regelflächen bilden die Berührpunkte der Fleknodaltangenten zwei projektiv ausgezeichnete Kurven, die Fleknodalkurven. In der vorliegenden Arbeit stellen wir die unterschiedlichen Behandelungen diesen ausgezeichneten Kurven in der Geschichte dar, und geben wir eine neue explizite Berechnung von den Fleknodal- bzw. LIE-Punkte auf der Basis einer PLÜCKER-Koordinaten-Darstellung der Regelfläche. Außerdem untersuchen wir die Fragestellungen, die man bekommt, wenn man versucht, dass das paarweise auftreten der LIE-Kurven irgendwie in Analogie zum klassischen euklidischen BERTRAND-Kurvenpaar zu stellen. Z.B. lässt sich die Frage nach Regelflächen, deren LIE-Kurven Orthogonaltrajektorien der Erzeugenden sind, hier beantwortet.
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