Induced Connections and Imbedded Riemannian Spaces

1956 ◽  
Vol 10 ◽  
pp. 15-25 ◽  
Author(s):  
Shoshichi Kobayashi
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Definition Of ◽  
Principal Fibre Bundle ◽  
The Right ◽  
Riemannian Spaces

Let P be a principal fibre bundle over M with group G and with projection π : P → M. By definition of a principal fibre bundle, G acts on P on the right. We shall denote this transformation law by ρ

Construction of N = 2 Supergravity on Principal Fibre Bundle

1988 ◽  
Vol 79 (6) ◽  
pp. 1431-1450 ◽  
Author(s):  
K. Kakazu ◽  
S. Matsumoto
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle

scholarly journals Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 242
Author(s):  
Simone Farinelli ◽  
Hideyuki Takada
Keyword(s):  
Cash Flow ◽  
Fibre Bundle ◽  
Asset Bubbles ◽  
Gauge Symmetries ◽  
Curvature Measures ◽  
Principal Fibre ◽  
Topological Obstructions ◽  
Principal Fibre Bundle ◽  
Risk Neutral Measures ◽  
No Free Lunch

Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”. The cash flow bundle is the associated vector bundle. The zero eigenspace of its connection Laplacian parameterizes all risk-neutral measures equivalent to the statistical one. A market satisfies the No-Free-Lunch-with-Vanishing-Risk (NFLVR) condition if and only if 0 is in the discrete spectrum of the Laplacian. The Jarrow–Protter–Shimbo theory of asset bubbles and their classification and decomposition extend to markets not satisfying the NFLVR. Euler’s characteristic of the asset nominal space and non-vanishing of the homology group of the cash flow bundle are both topological obstructions to NFLVR.

scholarly journals Supergravity on Principal Fibre Bundle

1987 ◽  
Vol 78 (4) ◽  
pp. 932-950 ◽  
Author(s):  
K. Kakazu ◽  
S. Matsumoto
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle

CONNECTIONS ON A PRINCIPAL FIBRE BUNDLE

2000 ◽  
pp. 303-371
Author(s):  
YVONNE CHOQUET-BRUHAT ◽  
CÉCILE DEWITT-MORETTE
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle

scholarly journals The Principal Fibre Bundle on Lorentzian Almost R-para Contact Structure

2021 ◽  
Vol 27_NS1 (1) ◽  
pp. 16-20
Author(s):  
Lovejoy S. Das ◽  
Mohammad Nazrul Islam Khan
Keyword(s):  
Lie Group ◽  
Tensor Field ◽  
Contact Structure ◽  
Principal Bundle ◽  
Fibre Bundle ◽  
Product Structure ◽  
Frame Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle ◽  
Almost Paracontact Structure

The purpose of this paper is to study the principal fibre bundle ( P , M , G , π p ) with Lie group G , where M admits Lorentzian almost paracontact structure ( Ø , ξ p , η p , g ) satisfying certain condtions on (1, 1) tensor field J , indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π * is the isomorphism.

scholarly journals On Invariant Connections over a Principal Fibre Bundle

1958 ◽  
Vol 13 ◽  
pp. 1-19 ◽  
Author(s):  
Hsien-Chung Wang
Keyword(s):  
Lie Group ◽  
Systematic Study ◽  
Fibre Bundle ◽  
Affine Connection ◽  
Holonomy Group ◽  
Coset Space ◽  
Multilinear Mappings ◽  
Principal Fibre ◽  
Invariant Affine Connection ◽  
Principal Fibre Bundle

The invariant affine connection over a coset space G/J of a Lie group G have been discussed by various authors. Recently, Nomizu [8] gave a systematic study of this problem when J is reductible in G. Among other results, he established a 1-1 correspondence between the invariant affine connections and certain multilinear mappings, and calculated the torsion and curvature. For canonical affine connection of the second kind, the holonomy group was also given.

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