منابع مشابه
The Hull of Rudin’s Klein Bottle
In 1981 Walter Rudin exhibited a totally real embedding of the Klein bottle into C2. We show that the polynomially convex hull of Rudin’s Klein bottle contains an open subset of C2. We also describe another totally real Klein bottle in C2 whose hull has topological dimension equal to three.
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In 1985 Montiel & Ros showed that the only minimal torus in S3, which first eigenvalue of the Laplacian is 2, is the Clifford torus. Here, we will show first the no existence of an embedded Klein bottle in RP, indeed we will prove that the only non orientable compact surfaces that can be embedded in RP are those with odd Euler characteristic. Later on, we will show another proof of Montiel & Ro...
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In this paper, we shall determine the complete list of irreducible quadrangulations of the Klein bottle. By this result, we can easily list all the minorminimal 2-representative graphs on the Klein bottle. Moreover, we shall show that any two bipartite quadrangulations of the Klein bottle with at least 10 vertices are transformed into each other by a sequence of diagonal slides and a sequence o...
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We show that an Eulerian triangulation of the Klein bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein bottle with facewidth at least four is 5-colorable.
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A triangulation of a closed surface is a simple graph embedded on the surface so that each face is triangular and that any two faces have at most one edge in common. (The latter is needed only for the sphere to exclude K3 from the spherical triangulations.) It is often regarded as a 2-simplicial complex together with its triangular faces. Two triangulations G and G$ of a closed surface F 2 are ...
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ژورنال
عنوان ژورنال: AI & SOCIETY
سال: 2021
ISSN: 0951-5666,1435-5655
DOI: 10.1007/s00146-021-01225-w