scholarly journals Classification of second order symmetric tensors in five‐dimensional Kaluza–Klein‐type theories

1995 ◽  
Vol 36 (6) ◽  
pp. 3074-3084 ◽  
Author(s):  
J. Santos ◽  
M. J. Rebouças ◽  
A. F. F. Teixeira
Keyword(s):  
Second Order ◽  
Symmetric Tensors ◽  
Kaluza Klein

scholarly journals A NOTE ON SEGRE TYPES OF SECOND-ORDER SYMMETRIC TENSORS IN 5-D BRANE-WORLD COSMOLOGY

2003 ◽  
Vol 18 (39) ◽  
pp. 2807-2815 ◽  
Author(s):  
M. J. REBOUÇAS ◽  
J. SANTOS
Keyword(s):  
Second Order ◽  
Brane World ◽  
Canonical Forms ◽  
Symmetric Tensors ◽  
Five Dimensions ◽  
Spatial Dimensions ◽  
Recent Developments ◽  
Segre Types ◽  
Matter Fields

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we re-examine the classification of the second-order symmetric tensors in 5-D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in five-dimensional spacetimes. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional (n>4) spaces from the classification on four-dimensional spaces. This is important in the context of 11-D supergravity and 10-D superstrings.

SATANIC AND THELEMIC CIRCLES ON KNOTS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350017 ◽  
Author(s):  
G. FLOWERS
Keyword(s):  
Geometric Interpretation ◽  
Second Order ◽  
Geometric Properties ◽  
Vassiliev Invariants ◽  
Vassiliev Invariant ◽  
Knot Diagrams

While Vassiliev invariants have proved to be a useful tool in the classification of knots, they are frequently defined through knot diagrams, and fail to illuminate any significant geometric properties the knots themselves may possess. Here, we provide a geometric interpretation of the second-order Vassiliev invariant by examining five-point cocircularities of knots, extending some of the results obtained in [R. Budney, J. Conant, K. P. Scannell and D. Sinha, New perspectives on self-linking, Adv. Math. 191(1) (2005) 78–113]. Additionally, an analysis on the behavior of other cocircularities on knots is given.

A classification of second-order technical progress operators

1984 ◽  
Vol 14 (2-3) ◽  
pp. 269-274 ◽  
Author(s):  
Joel D. Scheraga
Keyword(s):  
Technical Progress ◽  
Second Order

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification

On the classification of rational second-order Bézier curves

2008 ◽  
Vol 41 (2) ◽  
pp. 176-181
Author(s):  
M. I. Grigor’ev ◽  
V. N. Malozemov ◽  
A. N. Sergeev
Keyword(s):  
Second Order ◽  
Bezier Curves ◽  
Bézier Curves

scholarly journals Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 72
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri
Keyword(s):  
Gaussian Curvature ◽  
Tangent Bundle ◽  
Two Dimensional ◽  
Constant Gaussian Curvature ◽  
Metric Structures ◽  
Unit Tangent Bundle ◽  
Tangent Bundles ◽  
Full Classification ◽  
Kaluza Klein

In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

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