Parametric manifolds. I. Extrinsic approach
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifol...
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifol...
Quantum Heisenberg group and algebra: Contraction, left and right regular representations
It is shown that the quantum Heisenberg group Hq(1) can be obtained by means of contraction from the quantum SUq(2) group. Its dual Hopf algebra is the quantum Heisenberg algebra Uq(h(1)). Left and ri...
It is shown that the quantum Heisenberg group Hq(1) can be obtained by means of contraction from the quantum SUq(2) group. Its dual Hopf algebra is the quantum Heisenberg algebra Uq(h(1)). Left and ri...
Parametric manifolds. II. Intrinsic approach
J. Math. Phys. 36, 1394 (1995); doi:10.1063/1.531128
Issue Date: March 1995
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A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a new geometric object, called the deficiency, which behaves much like torsion, and which measures whether a parametric manifold can be viewed as a one-parameter family of orthogonal hypersurfaces. ©1995 American Institute of Physics.
| History: | Received 18 July 1994; accepted 24 August 1994 |
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http://link.aip.org/link/?JMAPAQ/36/1394/1 |
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KEYWORDS and PACS
MATHEMATICAL MANIFOLDS,
TENSOR FIELDS,
SURFACES,
DIFFERENTIAL GEOMETRY,
GENERAL RELATIVITY THEORY,
SPACE&minus,
TIME,
VECTOR FIELDS,
TORSION,
GRAVITATIONAL FIELDS,
RIEMANN SPACE
- 04.20.Cv
General relativity and gravitation Classical general relativity Fundamental problems and general formalism - 04.20.Ex
General relativity and gravitation Classical general relativity Initial value problem, existence and uniqueness of solutions - 02.40.Hw
Mathematical methods in physics Geometry, differential geometry, and topology Classical differential geometry - YEAR: 1995
PUBLICATION DATA
0022-2488 (print)
1089-7658 (online)
AIP
REFERENCES (10)
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“The method of timelike two-surfaces,” Differential Geometry and Mathematical Physics, Contemporary Mathematics, Vol. 170, edited by J. K. Beem and K. Duggal (American Mathematical Society, Providence, 1994).
