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1 
Extension theorem and its application to the Frenet formulas ofcurves黃炎明, Wong, Yimming. January 1966 (has links)
published_or_final_version / Mathematics / Master / Master of Science

2 
Differentialgeometric aspects of adapted contact structures.Pitucco, Anthony Peter. January 1991 (has links)
Let M denote a 2ndimensional 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 1forms {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 nonzero 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 subalgebra 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 nonconservative systems. A different set of 2n 1forms {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 parameterdependent 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.

3 
The integrogeometric tangent measures of euclidean nspace /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.

4 
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.

5 
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.

6 
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)FriedrichWilhelmsUniversität Berlin, 1861. / Vita.

7 
Ueber die Krümmung, Torsion und geodätische Krümmung der auf einer Fläche gezogenen CurvenRunge, Carl, January 1880 (has links)
Thesis (doctoral)FriedrichWilhelmsUniversität zu Berlin, 1880. / Vita.

8 
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)
ThesisUniversity of Leiden, 1919.

9 
Analytische theorie der ruimtekrommen ...Lem, Jacob Wouter. January 1899 (has links)
ProefschriftLeyden, 1899. / Stellingen included. "Literatuuroverzicht": p. [127]136.

10 
Extension theorem and its application to the Frenet formulas of curves /Wong, Yimming. January 1966 (has links)
Thesis (M. Sc.)University of Hong Kong, 1966. / Typewritten.

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