Displaying similar documents to “A short proof of a strong version of Poprużenko's Theorem”

Surfaces in 3-space that do not lift to embeddings in 4-space

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...

Embedded surfaces in the 3-torus

Allan L. Edmonds (2008)

Fundamenta Mathematicae

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Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the more involved case when the surface is nonorientable.

On surface braids of index four with at most two crossings

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.

Surfaces with prescribed Weingarten operator

Udo Simon, Konrad Voss, Luc Vrancken, Martin Wiehe (2002)

Banach Center Publications

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We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.

Timelike Christoffel pairs in the split-quaternions

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.