Delaunay surfaces expressed in terms of a Cartan moving frame
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Paul Bracken
Abstract
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 equations 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.
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Articles in the same Issue
- Frontmatter
- On the steady-states of a two-species non-local cross-diffusion model
- Iterative techniques with computer realization for initial value problems for Riemann–Liouville fractional differential equations
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Existence of positive solutions of a new class of nonlocal
- A function fitting method
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- Some properties of modified Szász–Mirakyan operators in polynomial spaces via the power summability method
- Some sufficient conditions for univalence and close-to-convexity
- Approximation by Stancu–Chlodowsky type λ-Bernstein operators
- Radius problems for univalent functions
- Convergence theorem for a finite family of asymptotically demicontractive multi-valued mappings in CAT(0) spaces
- Transforming linear time-varying optimal control problems with quadratic criteria into quadratic programming ones via wavelets
- Delaunay surfaces expressed in terms of a Cartan moving frame
