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Extension theorem and its application to the Frenet formulas ofcurves黃炎明, Wong, Yim-ming. January 1966 (has links)
published_or_final_version / Mathematics / Master / Master of Science
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Differential-geometric aspects of adapted contact structures.Pitucco, Anthony Peter. January 1991 (has links)
Let M denote a 2n-dimensional globally defined orientable manifold from which is constructed the product space N = M x R. It is assumed that N is endowed with a set of 2n independent smooth 1-forms {π(h),πʰ:h = 1,..,n}. Certain conditions are imposed on {π(h),πʰ} which imply the existence of local coordinates {qʰ,p(h)} on M and a function H(qʰ,p(h),t) on N, where t is the single coordinate on R, such that dπ = π(h) ∧ πʰ, where π has the structure of a Cartan form on N. The assumption that the function h = p(h)∂H/∂p(h)-H is non-zero on a region D ⊂ N, implies that π has maximal class on D. This construction gives rise to a local adapted contact structure on N and a local symplectic structure on M. A vector field X on N is said to be a contact field if there exists a smooth function σ : N → R such that ₤ₓπ = σπ. A vector field Z on N is called a canonical vector field if it admits the representation Z = ∂/∂t + (H, ) where (,) denotes the Poisson bracket on M. For a given function σ, a prescription is given for the construction of the space c(σ)(N) of contact fields in terms of solutions F of the p.d.e. Z<F> = σh. The vector space (UNFORMATTED EQUATION FOLLOWS) c(N) = ∪ (σ∊C)(∞)c(σ)(N) (END UNFORMATTED EQUATION) is shown to have the structure of a Lie sub-algebra of the Lie algebra of vector fields on N. It is shown that the associated subspace A(π) = {X:X˩π = 0} is such that c(σ)(N) ∩ A(π) = {0}. This implies that there is an X in c(σ)(N) such that X˩π ≠ 0. Thus, if the function H that appears in the Cartan form π is such that H = X˩π for any X ∊ c(σ)(N) it is possible to deduce that ∂H/∂t ≠ 0, which shows that such vector fields may be of relevance to the theory of non-conservative systems. A different set of 2n 1-forms {π(h),πʰ} is introduced on N that are subject to analogous conditions which ensure the existence of local coordinates (qʰ,p(h)) on M and a function K(qʰ,p(h),t) that gives rise to a new Cartan form π on N such that dπ= π(h) ∧ πʰ. By definition, the fundamental invariant of a parameter-dependent canonical transformation on N is dπ = dπ. In this new setting a contact field X satisfies the ₤ₓπ = σπ for some function σ: N to R. The relationship between the contact vector fields X and X is investigated in depth.
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The integro-geometric tangent measures of euclidean n-space /Zelver, Jack Solomon. January 1970 (has links)
Thesis (Ph. D.)--Oregon State University, 1970. / Typescript (photocopy). Includes bibliographical references (leaf 44). Also available on the World Wide Web.
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Plane nets with equal invariants ... /Nelson, Alfred Lewis, January 1900 (has links)
Thesis (Ph. D.)--University of Chicago, 1915. / Vita. "A Private edition distributed by the University of Chicago Libraries." "Reprinted from Rendiconti del Circolo matematico di Palermo, Vol. XLI, 1916." Includes bibliographical references. Also available on the Internet.
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Über solche Koordinatensysteme auf Flächen, bei denen die eine Schar von Parameterkurven auf der andern gleiche Stücke abschneidetMuth, Fritz. January 1912 (has links)
Thesis (doctoral)--K. Technische Hochschule zu München, 1912. / Includes bibliographical references.
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Demonstratio complurium Ill. Kummeri theorematum, quae agunt de generalibus, et infinite tenuibus luminis fascibus, praecipue in crystallisMeibauer, Rudolf Ottomar, January 1900 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität Berlin, 1861. / Vita.
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Ueber die Krümmung, Torsion und geodätische Krümmung der auf einer Fläche gezogenen CurvenRunge, Carl, January 1880 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1880. / Vita.
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Deformaties en trillingen in het vaste lichaam bij afwijkingen van de wet van Hooke ook in verband met de toestandsvergelijking ...Tresling, Jan Hendrik August Theunes. January 1919 (has links)
Thesis--University of Leiden, 1919.
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Analytische theorie der ruimtekrommen ...Lem, Jacob Wouter. January 1899 (has links)
Proefschrift--Leyden, 1899. / Stellingen included. "Literatuur-overzicht": p. [127]-136.
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Extension theorem and its application to the Frenet formulas of curves /Wong, Yim-ming. January 1966 (has links)
Thesis (M. Sc.)--University of Hong Kong, 1966. / Typewritten.
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