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c-Extensions of P- and T-Geometries

2001
*
Journal of combinatorial theory. Series A
*

We consider affine

doi:10.1006/jcta.2000.3077
fatcat:zwy7ksywlvawno5zorozciradm
*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. ...##
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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

doi:10.1017/s0008439500031866
fatcat:zw4soi6p3zgfrder6y2kobjhce
*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. ...##
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Extensions of combinatorial geometries by the addition of a unique line

1984
*
Journal of combinatorial theory. Series A
*

All

doi:10.1016/0097-3165(84)90017-7
fatcat:m5x5qxefvvfgtdoiycfjnqxpou
*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. ...##
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General construction of symmetric parabolic structures

2012
*
Differential geometry and its applications
*

We provide construction

doi:10.1016/j.difgeo.2012.06.006
fatcat:5gz4dmdtgffrro2twcouqb4me4
*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*). ...##
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Generalized towers of flag-transitive circular extensions of a non-classical C3-geometry

1994
*
Journal of combinatorial theory. Series A
*

It was first found by Neumaier I-7]

doi:10.1016/0097-3165(94)90069-8
fatcat:e673v64oofaoriyv5u6yxn6bje
*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 ...##
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Geometric structures invariant to symmetries
[article]

2012
*
arXiv
*
pre-print

Then we investigate the case

arXiv:1207.0193v1
fatcat:bsn76vd6s5e2ldtfihhu77b6d4
*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. ...##
###
Some Polar Towers

1991
*
European journal of combinatorics (Print)
*

In this sense, if I say that the (e k •

doi:10.1016/s0195-6698(13)80016-9
fatcat:2uxsqgas4vgybiy6l7fbkgyeru
*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 . ...##
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Cartan geometries modeled on skeletons and morphisms induced by extension functors
[article]

2016
*
arXiv
*
pre-print

Some examples

arXiv:1602.02019v1
fatcat:zj332ihjvnevfo56tmcxk2gfri
*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 . ...##
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5-dimensional geometries III: the fibered geometries
[article]

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 , ...

##
###
On local Calabi–Yau supermanifolds and their mirrors

2006
*
Journal of Physics A: Mathematical and General
*

studied

doi:10.1088/0305-4470/39/20/022
fatcat:rzz543hkqzh4lgexgglsfwvfi4
*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. ...##
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Effects of non-extensive electrons and positive/negative dust particles on modulational instability of dust-ion-acoustic solitary waves in non-planar geometry

2016
*
Pramana (Bangalore)
*

It is found that the basic features

doi:10.1007/s12043-016-1309-4
fatcat:beevcqvrqzeeheqg3tpdltxlku
*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. ...##
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On symmetric CR geometries of hypersurface type
[article]

2018
*
arXiv
*
pre-print

We construct examples

arXiv:1707.07531v3
fatcat:jp4byan6ifcu3oatydgnn2hnay
*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. ...##
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Regular 2-Graphs and Extensions of Partial Geometries

1991
*
European journal of combinatorics (Print)
*

We study so-called 2-graph

doi:10.1016/s0195-6698(13)80078-9
fatcat:jynx7vrbunhalalefspjjsqydy
*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. ...##
###
Closure Operators and Lattice Extensions

2004
*
Order
*

For closure operators Γ

doi:10.1007/s11083-004-5178-y
pmid:15127974
fatcat:ryx2z4aof5a53oi6v2ot6k3mbi
*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*t*∈*T*D 0 tK . ...##
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Extension Phenomena for Holomorphic Geometric Structures

2009
*
Symmetry, Integrability and Geometry: Methods and Applications
*

The most commonly encountered types

doi:10.3842/sigma.2009.058
fatcat:kfmvzc6jfrgezikehhn32ozplu
*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*and*•*P*1 ×*P*1 \diagonal-*geometries*; see Example 5.26 ...
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