A Parameterization of the Klein Bottle by Isometric Transformations in with Mathematica

2021 ◽  
pp. 261-272
Author(s):  
Ricardo Velezmoro-León ◽  
Nestor Javier Farias-Morcillo ◽  
Robert Ipanaqué-Chero ◽  
José Manuel Estela-Vilela ◽  
Judith Keren Jiménez-Vilcherrez
Keyword(s):  
Klein Bottle

scholarly journals Constructing the Graphs That Triangulate Both the Torus and the Klein Bottle

1999 ◽  
Vol 77 (1) ◽  
pp. 211-218 ◽  
Author(s):  
Serge Lawrencenko ◽  
Seiya Negami
Keyword(s):  
Klein Bottle

AUTOMORPHISMS OF BRAID GROUPS ON S2, T2, P2 AND THE KLEIN BOTTLE K

2008 ◽  
Vol 17 (01) ◽  
pp. 47-53 ◽  
Author(s):  
PING ZHANG
Keyword(s):  
Braid Group ◽  
Mapping Class Group ◽  
Class Group ◽  
Klein Bottle ◽  
Closed Surface ◽  
Group Extension ◽  
Braid Groups ◽  
Mapping Class ◽  
Group B ◽  
Central Automorphisms

It is shown that for the braid group Bn(M) on a closed surface M of nonnegative Euler characteristic, Out (Bn(M)) is isomorphic to a group extension of the group of central automorphisms of Bn(M) by the extended mapping class group of M, with an explicit and complete description of Aut (Bn(S2)), Aut (Bn(P2)), Out (Bn(S2)) and Out (Bn(P2)).

Enumeration of unsensed r-regular maps on the projective plane and the Klein bottle

2021 ◽  
Vol 344 (11) ◽  
pp. 112528
Author(s):  
Evgeniy Krasko ◽  
Alexander Omelchenko
Keyword(s):  
Projective Plane ◽  
Klein Bottle ◽  
Regular Maps

scholarly journals The 2-extendability of 5-connected graphs on the Klein bottle

2010 ◽  
Vol 310 (19) ◽  
pp. 2510-2518 ◽  
Author(s):  
Seiya Negami ◽  
Yusuke Suzuki
Keyword(s):  
Klein Bottle ◽  
Connected Graphs

scholarly journals DOUBLES OF KLEIN SURFACES

2012 ◽  
Vol 54 (3) ◽  
pp. 507-515
Author(s):  
ANTONIO F. COSTA ◽  
WENDY HALL ◽  
DAVID SINGERMAN
Keyword(s):  
Klein Bottle ◽  
Orientable Surface ◽  
Historical Note ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Algebraic Functions ◽  
Genus 2

Historical note. A non-orientable surface of genus 2 (meaning 2 cross-caps) is popularly known as the Klein bottle. However, the term Klein surface comes from Felix Klein's book “On Riemann's Theory of Algebraic Functions and their Integrals” (1882) where he introduced such surfaces in the final chapter.

scholarly journals OPEN DESCENDANTS OF U(2N) ORBIFOLDS AT RATIONAL RADII

2001 ◽  
Vol 16 (22) ◽  
pp. 3659-3671 ◽  
Author(s):  
A. N. SCHELLEKENS ◽  
N. SOUSA
Keyword(s):  
Klein Bottle ◽  
Charge Conjugation ◽  
Boundary States ◽  
Simple Currents

We construct explicitly the open descendants of some exceptional automorphism invariants of U (2N) orbifolds. We focus on the case N = p1 × p2, p1 and p2 prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R2 = 2p1/p2. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.

KALUZA–KLEIN BOTTLE COUPLED TO TOLMAN–HAWKING WORMHOLE

1991 ◽  
Vol 06 (17) ◽  
pp. 1547-1552
Author(s):  
A. DAVIDSON ◽  
Y. VERBIN
Keyword(s):  
Scalar Field ◽  
Klein Bottle ◽  
Gauge Coupling ◽  
Coupling Constants ◽  
Five Dimensions ◽  
Symmetric Configuration ◽  
Kaluza Klein

Asymptotically Euclidean regions connected by a wormhole may differ by their associated gauge coupling constants. This idea is realized in a field-theoretical manner using a conformally coupled scalar field in five dimensions. An SO (4) × U (1) e.m. -symmetric configuration is derived, describing a Kaluza–Klein bottle coupled to a Tolman–Hawking wormhole.

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