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c-Extensions of P- and T-Geometries

Gernot Stroth, Corinna Wiedorn
2001 Journal of combinatorial theory. Series A  
We consider affine extensions of geometries of Petersen and of tilde type, i.e., of flag-transitive geometries 1 belonging to a diagram where either bwwb X =bwwb P* , i.e., the geometry of edges and vertices  ...  Since there are no P-geometries of rank 5 and no T-geometries of rank 5 satisfying (V), this forces n 6.  ...  We thank Antonio and his institue for their hospitality and Antonio for many fruitful discussions which sometimes gave us more insight into the problems from a geometric point of view.  ... 
doi:10.1006/jcta.2000.3077 fatcat:zwy7ksywlvawno5zorozciradm

Lectures on the Calculus of Variations, by O. Bolza. 2nd edition. Dover Publications Inc., New York, 1961. ix + 271 pages. $1.65. - Lectures on the Calculus of Variations, by O. Bolza. 2nd edition. Chelsea Publishing Company, New York, 1961 (1904). ix + 271 pages. $1. 19. - The Calculus of Finite Differences, by G. Boole. Edited by J. F. Moulton. Fourth edition. Reprint 1960 from 1872 edition. Chelsea Publishing Company, New York, 1960. $1. 39. Cloth $3.95. - The Mathematical Theory of Non-uniform Gases, by ...

1963 Canadian mathematical bulletin  
behavior of the medium. The concluding chapter, titled Elastic and Hyperelastic Materials, discusses more general elastic behavior of materials and concludes with a section on stability.  ...  Algebraical and Topological Foundations of Geometry, H, Freudenthal (Ed. ).  ...  Macmillan Company of Canada, ix + 270 pages. $2. 95. An Index of Mathematical Tables, by A. Fletcher, J. C. P. Miller, L. Rosenhead, L.J. Comrie. Vol. I, Index According to Functions, xi + 608 pages.  ... 
doi:10.1017/s0008439500031866 fatcat:zw4soi6p3zgfrder6y2kobjhce

Extensions of combinatorial geometries by the addition of a unique line

Francesco Mazzocca
1984 Journal of combinatorial theory. Series A  
All extensions of a combinatorial geometry G are determined which can be obtained adjoining a unique line.  ...  The result is achieved investigating Dilworth structures and modular cuts of Dilworth truncation of G.  ...  Let p, q be points in R belonging to C (7 V and C n V', respectively. If p, q belong to the same line t(B,), then C E r, since t(B,) s C and t(Bi) E 7.  ... 
doi:10.1016/0097-3165(84)90017-7 fatcat:m5x5qxefvvfgtdoiycfjnqxpou

General construction of symmetric parabolic structures

Jan Gregorovič
2012 Differential geometry and its applications  
We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained  ...  Further, we investigate the case of parabolic contact geometries in great detail and we provide the full classification of those with semisimple groups of symmetries without complex factors.  ...  Then it is extension of homogeneous model G → G/K . Let (P → M, ω) be a Cartan geometry of type (L, P ).  ... 
doi:10.1016/j.difgeo.2012.06.006 fatcat:5gz4dmdtgffrro2twcouqb4me4

Generalized towers of flag-transitive circular extensions of a non-classical C3-geometry

Antonio Pasini, Satoshi Yoshiara
1994 Journal of combinatorial theory. Series A  
It was first found by Neumaier I-7] and called the Neumaier geometry in I-4, p. 258].  ...  Towers of flag-transitive circular extensions of C,-geometries are completely classified by [5] for n ~> 3 and for classical C2-geometry modulo some special cases.  ...  imply that (~, c5 p, c((eSP)*)) and (5 °, c(SP*), c((eS~)*)) are all the maximal generalized towers of flag-transitive circular extensions of the sporadic AT-geometry, where e(5 p*) and c((cSf)*) are the  ... 
doi:10.1016/0097-3165(94)90069-8 fatcat:e673v64oofaoriyv5u6yxn6bje

Geometric structures invariant to symmetries [article]

Jan Gregorovič
2012 arXiv   pre-print
Then we investigate the case of symmetric parabolic geometries in detail and obtain classification of symmetric AHS-structures and symmetric parabolic contact geometries in the semisimple cases.  ...  We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries.  ...  Any extension of (K, H) to (G, P ) induces extension of (K c , H c ) to (G, P ). Example 1.4.6.  ... 
arXiv:1207.0193v1 fatcat:bsn76vd6s5e2ldtfihhu77b6d4

Some Polar Towers

Thomas Meixner
1991 European journal of combinatorics (Print)  
In this sense, if I say that the (e k • C z ) geometry G is an extension of the (c' . C z ) geometry G' (0::;; t « k -1), that means that residues of type (c'> C z ) in G are isomorphic to G'.  ...  C z ) geometries are the ones for U 4(2) , Sp4(2) and Q(;(2); for Sp4(3), U 4 (3) and .0(; (3) . We want to determine the extension of these .  ... 
doi:10.1016/s0195-6698(13)80016-9 fatcat:2uxsqgas4vgybiy6l7fbkgyeru

Cartan geometries modeled on skeletons and morphisms induced by extension functors [article]

Jan Gregorovič
2016 arXiv   pre-print
Some examples and applications of the morphisms induced by extension functors are presented in the setting of the Riemannian geometries.  ...  We study how to compute (infinitesimal) automorphisms of Cartan geometries modeled on skeletons and how to compute the morphisms induced by the extension functors for particular Cartan geometries.  ...  Let (P 1 M → M, ω) be a Cartan geometry of type (R n ⊕gl(n), Gl(n), Ad) satisfying T = 0 and (G(u) → M, ω u ) be the holonomy reduction of (P 1 M → M, ω) at u ∈ P 1 M .  ... 
arXiv:1602.02019v1 fatcat:zj332ihjvnevfo56tmcxk2gfri

5-dimensional geometries III: the fibered geometries [article]

Andrew Geng
2016 arXiv   pre-print
and the non-maximal geometry SO(4)/SO(2) realized by two distinct maximal geometries.  ...  We classify the 5-dimensional homogeneous geometries in the sense of Thurston.  ...  If M = G/G p is a 5-dimensional model geometry for which G p T p M decomposes into 1-dimensional and 2-dimensional summands, then G is an extension f : isom M → R r ij → c(r jk , r ki ) t i → c(r ji ,  ... 
arXiv:1605.07546v1 fatcat:bsvbaeeztjdrjgoh2cjnwelgqa

On local Calabi–Yau supermanifolds and their mirrors

R Ahl Laamara, A Belhaj, L B Drissi, E H Saidi
2006 Journal of Physics A: Mathematical and General  
studied and explicit results are given for local A_r super-geometries.  ...  Solving the usual super- CY condition, requiring the equality of the total U(1) gauge charges of bosons Φ_b and the ghost like fields Ψ_f one ∑_bq_b=∑_fQ_f, as ∑_bq_b=0 and ∑_fQ_f=0, several examples are  ...  Acknowledgement 1 : AB would like to thank C. Vafa for kind hospitality at Harvard University, where a part of this work is done. We thank J. Rasmussen and A.  ... 
doi:10.1088/0305-4470/39/20/022 fatcat:rzz543hkqzh4lgexgglsfwvfi4

Effects of non-extensive electrons and positive/negative dust particles on modulational instability of dust-ion-acoustic solitary waves in non-planar geometry

M EGHBALI, B FAROKHI, M ESLAMIFAR
2016 Pramana (Bangalore)  
It is found that the basic features of the DIA waves are significantly modified by non-extensive electron distribution, polarity of the net dust-charge number density and non-planar geometry.  ...  The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive  ...  R c ln √ R c + √ R c − 1 √ R c − √ R c − 1 = 4 R c − 1. (37) The signs of parameters P and Q are important for understanding the physics of solitary waves and instability.  ... 
doi:10.1007/s12043-016-1309-4 fatcat:beevcqvrqzeeheqg3tpdltxlku

On symmetric CR geometries of hypersurface type [article]

Jan Gregorovič, Lenka Zalabová
2018 arXiv   pre-print
We construct examples of simply connected flat non-degenerate symmetric CR geometries of hypersurface type that do not carry a pseudo-Riemannian metric compatible with the symmetries.  ...  We show that non-flat non-degenerate symmetric CR geometries of hypersurface type are covered by CR geometries with a compatible pseudo-Riemannian metric preserved by all symmetries.  ...  Differentiation of the equality c(t) = S c(t) c(t) gives X = d dt | t=0 S c(t) (c(t)) = d dt | t=0 S c(t) (x) + T x S x .X, and we get d dt | t=0 S c(t) (x) = X − T x S x .X = 2X.  ... 
arXiv:1707.07531v3 fatcat:jp4byan6ifcu3oatydgnn2hnay

Regular 2-Graphs and Extensions of Partial Geometries

W.H. Haemers
1991 European journal of combinatorics (Print)  
We study so-called 2-graph geometries. These are geometries that carry a regular 2-graph, but also constitute I-point extensions of partial geometries .  ...  First we develop some theory; then we go through lists of known regular 2-graphs and partial geometries in order to find examples.  ...  ACKNOWLEDGEMENTS We thank Frank De Clerck and Hennie Wilbrink for several useful discussions.  ... 
doi:10.1016/s0195-6698(13)80078-9 fatcat:jynx7vrbunhalalefspjjsqydy

Closure Operators and Lattice Extensions

J. B. Nation
2004 Order  
For closure operators Γ and ∆ on the same set X, we say that ∆ is a weak (resp. strong) extension of Γ if Cl(X, Γ) is a complete meet-subsemilattice (resp. complete sublattice) of Cl(X, ∆).  ...  This context is used to describe describe the extensions of a finite lattice that preserve various properties.  ...  A set C ⊆ J is Γ S -closed iff for every a ∈ K, if D 0 aK ⊆ C then J aK ⊆ C. 2. For all T ⊆ J and every p ∈ J, p ≤ K K T if and only if p ≤ S S tT D 0 tK .  ... 
doi:10.1007/s11083-004-5178-y pmid:15127974 fatcat:ryx2z4aof5a53oi6v2ot6k3mbi

Extension Phenomena for Holomorphic Geometric Structures

Benjamin McKay
2009 Symmetry, Integrability and Geometry: Methods and Applications  
The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.  ...  The author is grateful to the editors, and to Sorin Dumitrescu, Sergei Ivashkovich and anonymous reviewers for their assistance in improving this paper.  ...  Among Cartan geometries on surfaces, this theorem applies to • C 2 -geometries, for any of the various complex Lie groups acting transitively on C 2 andP 1 × P 1 \diagonal-geometries; see Example 5.26  ... 
doi:10.3842/sigma.2009.058 fatcat:kfmvzc6jfrgezikehhn32ozplu
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