Point equivalence of functions on the 1-jet space J 1ℝ

2014 ◽  
Vol 48 (4) ◽  
pp. 250-255 ◽  
Author(s):  
P. V. Bibikov
Keyword(s):  
Jet Space

scholarly journals On holomorphic maps with only fold singularities

2001 ◽  
Vol 164 ◽  
pp. 147-184
Author(s):  
Yoshifumi Ando
Keyword(s):  
Homotopy Class ◽  
Homotopy Equivalent ◽  
Line Bundles ◽  
Jet Space ◽  
Complex Manifolds ◽  
Holomorphic Maps ◽  
Regular Map ◽  
Holomorphic Map ◽  
Fold Map ◽  
Tangent Bundles

Let f : N ≡ P be a holomorphic map between n-dimensional complex manifolds which has only fold singularities. Such a map is called a holomorphic fold map. In the complex 2-jet space J2(n,n;C), let Ω10 denote the space consisting of all 2-jets of regular map germs and fold map germs. In this paper we prove that Ω10 is homotopy equivalent to SU(n + 1). By using this result we prove that if the tangent bundles TN and TP are equipped with SU(n)-structures in addition, then a holomorphic fold map f canonically determines the homotopy class of an SU(n + 1)-bundle map of TN ⊕ θN to TP⊕ θP, where θN and θP are the trivial line bundles.

North Star Plasma-Jet Space Experiment

2004 ◽  
Vol 41 (4) ◽  
pp. 483-489 ◽  
Author(s):  
R. E. Erlandson ◽  
C. I. Meng ◽  
P. K. Swaminathan ◽  
C. K. Kumar ◽  
V. K. Dogra ◽  
...  
Keyword(s):  
Plasma Jet ◽  
Space Experiment ◽  
Jet Space

scholarly journals GEOMETRIC STRUCTURES OF THE CLASSICAL GENERAL RELATIVISTIC PHASE SPACE

2008 ◽  
Vol 05 (05) ◽  
pp. 699-754 ◽  
Author(s):  
JOSEF JANYŠKA ◽  
MARCO MODUGNO
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Relativistic Particle ◽  
Jet Space ◽  
Geometric Structures ◽  
Geometric Properties ◽  
Geometric Conditions ◽  
General Relativistic ◽  
Relativistic Phase

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1-dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialize these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

Jets of differential equations having integrable extensions

1998 ◽  
Vol 18 (6) ◽  
pp. 1527-1544
Author(s):  
MASSIMO VILLARINI
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
First Integral ◽  
Jet Space ◽  
Analytic First Integral

We characterize the set of $n$-jets admitting an extension which is a germ of a differential equation with an analytic first integral, and compute its codimension in the $n$-jet space. Some applications in the case of the centre-focus problem are given.

scholarly journals Feature extraction on local jet space for texture classification

2015 ◽  
Vol 439 ◽  
pp. 160-170 ◽  
Author(s):  
Marcos William da Silva Oliveira ◽  
Núbia Rosa da Silva ◽  
Antoine Manzanera ◽  
Odemir Martinez Bruno
Keyword(s):  
Feature Extraction ◽  
Texture Classification ◽  
Jet Space

On real simple singularities

1980 ◽  
Vol 88 (2) ◽  
pp. 273-279 ◽  
Author(s):  
J. W. Bruce ◽  
P. J. Giblin
Keyword(s):  
Topological Invariant ◽  
Milnor Number ◽  
Jet Space ◽  
Complex Singularity ◽  
Simple Singularities ◽  
The Right ◽  
Th 1

In (3), Cor. 2 to Th. 1, the first author proved that in the complex jet space Jk (n, 1) the orbits of simple singularities form canonical strata. By definition the canonical stratification is contact invariant so the proof consisted essentially of two steps: firstly, any two functions in the same canonical stratum are C0-equivalent by right-left changes of coordinates, and secondly, the right codimension (and hence the Milnor number) of an isolated complex singularity is a topological invariant.

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