Displaying similar documents to “The catenary (almost) everywhere.”

The rectifying developable and the spherical Darboux image of a space curve

Shyuichi Izumiya, Haruyo Katsumi, Takako Yamasaki (1999)

Banach Center Publications

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In this paper we study singularities of certain surfaces and curves associated with the family of rectifying planes along space curves. We establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices.

Ruled W-surfaces in Minkowski 3-space ℜ 1 3

Rashad A. Abdel-Baky, H. N. Abd-Ellah (2008)

Archivum Mathematicum

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In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set { K , K I I , H , H I I } , where ( K , H ) and ( K I I , H I I ) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.

Ruled W-surfaces in Minkowski 3-space ℜ 1 3

Rashad A. Abdel-Baky, H. N. Abd-Ellah (2008)

Archivum Mathematicum

Similarity:

In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set { K , K I I , H , H I I } , where ( K , H ) and ( K I I , H I I ) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.

Non-trivial Ш in the Jacobian of an infinite family of curves of genus 2

Anna Arnth-Jensen, E. Victor Flynn (2009)

Journal de Théorie des Nombres de Bordeaux

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We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.