Projective invariance and the fifth coordinate

1975 ◽  
Vol 18 (7) ◽  
pp. 966-970
Author(s):  
G. S. Asanov
Keyword(s):  
Projective Invariance

scholarly journals On the N-pion extension of the Lovelace-Shapiro model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Massimo Bianchi ◽  
Dario Consoli ◽  
Paolo Di Vecchia
Keyword(s):  
Extra Dimensions ◽  
Tree Level ◽  
Negative Norm ◽  
Projective Invariance ◽  
Non Linear ◽  
Point Amplitude

Abstract We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear σ-model for α′ → 0 keeping Fπ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons.

A NOTE ON SPRAYS OF ISOTROPIC CURVATURE

2021 ◽  
Vol 21 (3) ◽  
pp. 783-788
Author(s):  
MURADİYE ÇİMDİKER ASLAN ◽  
YASİN ÜNLÜTÜRK ◽  
CUMALİ EKİCİ
Keyword(s):  
Weyl Curvature ◽  
Ricci Flat ◽  
Projective Invariance ◽  
Basic Goal ◽  
Isotropic Curvature ◽  
The Mean

A basic goal of this paper is to calculate, Weyl curvature of R-flat (Ricci-flat) spray of isotropic curvature and a locally projectively R-flat (Ricci-flat) spray, which is a projective invariance. Besides, the equivalents of E ̅-curvature and H-curvature that are closely related to the mean Berwald curvature have been found for a locally projectively R-flat spray of isotropic curvature.

scholarly journals Rigidity through a Projective Lens

2021 ◽  
Vol 11 (24) ◽  
pp. 11946
Author(s):  
Anthony Nixon ◽  
Bernd Schulze ◽  
Walter Whiteley
Keyword(s):  
Geometric Reasoning ◽  
Multivariate Splines ◽  
Infinitesimal Rigidity ◽  
Singular Configurations ◽  
Projective Invariance ◽  
Projective Representations ◽  
Discrete Structures ◽  
Static Rigidity

In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar–joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body–hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.

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