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Full-Text Articles in Physical Sciences and Mathematics
Delaunay Surfaces Expressed In Terms Of A Cartan Moving Frame, Paul Bracken
Delaunay Surfaces Expressed In Terms Of A Cartan Moving Frame, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Delaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equation which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.
Cartan’S Approach To Second Order Ordinary Differential Equations, Paul Bracken
Cartan’S Approach To Second Order Ordinary Differential Equations, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In his work on projective connections, Cartan discusses his theory of second order differential equations. It is the aim here to look at how a normal projective connection can be constructed and how it relates to the geometry of a single second order differential equation. The calculations are presented in some detail in order to highlight the use of gauge conditions