Holmorphic Automorphism Group of a Sort of Three Dimensional Hopf Manifold

2011 ◽  
pp. 61-65
Keyword(s):  
Automorphism Group ◽  
Three Dimensional ◽  
Hopf Manifold

Automorphism groups of 3-dimensional complex tori

1999 ◽  
Vol 1999 (508) ◽  
pp. 99-125 ◽  
Author(s):  
Ch Birkenhake ◽  
V González ◽  
H Lange
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Three Dimensional ◽  
Maximal Order ◽  
3 Dimensional ◽  
Complex Tori

Abstract We compute all finite automorphism groups of three-dimensional complex tori which are maximal in the isogeny class. The maximal order of such an automorphism group is 1296.

scholarly journals COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p3

2012 ◽  
Vol 11 (05) ◽  
pp. 1250100 ◽  
Author(s):  
DYLENE AGDA SOUZA DE BARROS ◽  
ALEXANDER GRISHKOV ◽  
PETR VOJTĚCHOVSKÝ
Keyword(s):  
Automorphism Group ◽  
Abelian Groups ◽  
Three Dimensional ◽  
Isomorphism Classes ◽  
Trivial Center ◽  
One To One ◽  
Nilpotent Class

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by [Formula: see text] the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z ≅ ℤp such that Q/Z ≅ ℤp × ℤp. Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop Fp in the variety of loops whose elements have order dividing p2 and whose associators have order dividing p, we show that every loop of [Formula: see text] is a quotient of Fp by a central subloop of order p3. The automorphism group of Fp induces an action of GL 2(p) on the three-dimensional subspaces of Z(Fp) ≅ (ℤp)4. The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from [Formula: see text]. We describe the orbits, and hence we classify the loops of [Formula: see text] up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing [Formula: see text] up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p3. There are precisely seven commutative automorphic loops of order p3 for every prime p, including the three abelian groups of order p3.

scholarly journals Sectional and Ricci Curvature for Three-Dimensional Lie Groups

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Gerard Thompson ◽  
Giriraj Bhattarai
Keyword(s):  
Automorphism Group ◽  
Lie Groups ◽  
Ricci Curvature ◽  
Lie Group ◽  
Systematic Study ◽  
Three Dimensional ◽  
Invariant Metrics ◽  
Curvature Function ◽  
Invariant Metric ◽  
Curvature Tensors

Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.

scholarly journals TETRAVALENT s-TRANSITIVE GRAPHS OF ORDER TWICE A PRIME POWER

2010 ◽  
Vol 88 (2) ◽  
pp. 277-288 ◽  
Author(s):  
JIN-XIN ZHOU ◽  
YAN-QUAN FENG
Keyword(s):  
Automorphism Group ◽  
Bipartite Graph ◽  
Projective Geometry ◽  
Prime Power ◽  
Complete Bipartite Graph ◽  
Three Dimensional ◽  
Transitive Graph ◽  
Incidence Graph ◽  
Normal Cover ◽  
Transitive Graphs

AbstractA graph is s-transitive if its automorphism group acts transitively on s-arcs but not on (s+1)-arcs in the graph. Let X be a connected tetravalent s-transitive graph of order twice a prime power. In this paper it is shown that s=1,2,3 or 4. Furthermore, if s=2, then X is a normal cover of one of the following graphs: the 4-cube, the complete graph of order 5, the complete bipartite graph K5,5 minus a 1-factor, or K7,7 minus a point-hyperplane incidence graph of the three-dimensional projective geometry PG(2,2); if s=3, then X is a normal cover of the complete bipartite graph of order 4; if s=4, then X is a normal cover of the point-hyperplane incidence graph of the three-dimensional projective geometry PG(2,3). As an application, we classify the tetravalent s-transitive graphs of order 2p2 for prime p.

Automorphism Groups of Connected Cubic Cayley Graphs of Order 4p

2007 ◽  
Vol 14 (02) ◽  
pp. 351-359 ◽  
Author(s):  
Chuixiang Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Dihedral Group ◽  
Automorphism Groups ◽  
Regular Representation ◽  
Cayley Graphs ◽  
Three Dimensional ◽  
Group A ◽  
The Right

For a prime p, let D4p be the dihedral group 〈a,b | a2p = b2 = 1, b-1ab = a-1〉 of order 4p, and Cay (G,S) a connected cubic Cayley graph of order 4p. In this paper, it is shown that the automorphism group Aut ( Cay (G,S)) of Cay (G,S) is the semiproduct R(G) ⋊ Aut (G,S), where R(G) is the right regular representation of G and Aut (G,S) = {α ∈ Aut (G) | Sα = S}, except either G = D4p (p ≥ 3), Sβ = {b,ab,apb} for some β ∈ Aut (D4p) and [Formula: see text], or Cay (G,S) is isomorphic to the three-dimensional hypercube Q3[Formula: see text] and G = ℤ4 × ℤ2 or D8.

scholarly journals Lacunary Möbius Fractals on the Unit Disk

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 91
Author(s):  
L. K. Mork ◽  
Keith Sullivan ◽  
Darin J. Ulness
Keyword(s):  
Automorphism Group ◽  
Unit Disk ◽  
Parameter Space ◽  
Rotational Symmetry ◽  
Julia Sets ◽  
Three Dimensional ◽  
Open Unit ◽  
Open Unit Disk ◽  
Dimensional Parameter ◽  
Mandelbrot Sets

Centered polygonal lacunary functions are a type of lacunary function that exhibit behaviors that set them apart from other lacunary functions, this includes rotational symmetry. This work will build off of earlier studies to incorporate the automorphism group of the open unit disk D, which is a subgroup of the Möbius transformations. The behavior, dimension, dynamics, and sensitivity of filled-in Julia sets and Mandelbrot sets to variables will be discussed in detail. Additionally, several visualizations of this three-dimensional parameter space will be presented.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Sign in / Sign up

Export Citation Format

Share Document