About the geometry of milling paths.
Szilvási-Nagy, Márta, Béla, Szilvia, Mátyási, Gyula (2008)
Annales Mathematicae et Informaticae
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Szilvási-Nagy, Márta, Béla, Szilvia, Mátyási, Gyula (2008)
Annales Mathematicae et Informaticae
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Sinclair, Robert, Tanaka, Minoru (2002)
Experimental Mathematics
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Robert Connelly (1977)
Publications Mathématiques de l'IHÉS
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J. Carter, Masahico Saito (1998)
Banach Center Publications
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A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic...
Ulmet, Dan-Eugen (2004)
International Journal of Mathematics and Mathematical Sciences
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Hoffman, David, Wei, Fusheng (2002)
Experimental Mathematics
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M. P. Dussan, M. Magid (2010)
Annales Polonici Mathematici
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We characterize the Christoffel pairs of timelike isothermic surfaces in the four-dimensional split-quaternions. When restricting the receiving space to the three-dimensional imaginary split-quaternions, we establish an equivalent condition for a timelike surface in ℝ³₂ to be real or complex isothermic in terms of the existence of integrating factors.
Maher, Joseph (2005)
Geometry & Topology
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R. E. Barnhill (1992)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Teruo Nagase, Akiko Shima (2005)
Fundamenta Mathematicae
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Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.
O. Karwowski (1964)
Annales Polonici Mathematici
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Roytburd, V. (1983)
International Journal of Mathematics and Mathematical Sciences
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Alex Eskin, Howard Masur, Anton Zorich (2003)
Publications Mathématiques de l'IHÉS
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A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description...