On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space.
Kalikakis, Dimitrios E. (2002)
Abstract and Applied Analysis
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Displaying similar documents to “A characterization of regular saddle surfaces in the hyperbolic and spherical three-space.”
On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space.
Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature
Rafael López, Esma Demir (2014)
Open Mathematics
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We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
Surfaces of characteristic curvature
Vladimír Fiřt (1974)
Aplikace matematiky
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Geodesic curvature of curves on surfaces in equiaffine space
Bruno Budinský (1968)
Časopis pro pěstování matematiky
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Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes Application to the Minkowski problem in the Minkowski space
Thierry Barbot, François Béguin, Abdelghani Zeghib (2011)
Annales de l’institut Fourier
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We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with constant Gauss curvature. In the constant negative curvature case, such a foliation exists outside the convex core. The existence of these foliations, together with a theorem...
Polynomial translation surfaces of Weingarten types in Euclidean 3-space
Dae Yoon (2010)
Open Mathematics
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In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect to the Gaussian curvature, the mean curvature and the second Gaussian curvature.
Invariants and Bonnet-type theorem for surfaces in ℝ4
Georgi Ganchev, Velichka Milousheva (2010)
Open Mathematics
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...