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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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

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.

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.

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.

Über solche Koordinatensysteme auf Flächen, bei denen die eine Schar von Parameterkurven auf der andern gleiche Stücke abschneidet

Muth, Fritz. January 1912 (has links)
Thesis (doctoral)--K. Technische Hochschule zu München, 1912. / Includes bibliographical references.

Demonstratio complurium Ill. Kummeri theorematum, quae agunt de generalibus, et infinite tenuibus luminis fascibus, praecipue in crystallis

Meibauer, Rudolf Ottomar, January 1900 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität Berlin, 1861. / Vita.

Ueber die Krümmung, Torsion und geodätische Krümmung der auf einer Fläche gezogenen Curven

Runge, Carl, January 1880 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1880. / Vita.

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.

Analytische theorie der ruimtekrommen ...

Lem, Jacob Wouter. January 1899 (has links)
Proefschrift--Leyden, 1899. / Stellingen included. "Literatuur-overzicht": p. [127]-136.

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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