A teleparallel geometry is an n-dimensional manifold equipped with a frame basis and an independent spin connection. For such a geometry, the curvature tensor vanishes and the torsion tensor is non-zero. A straightforward approach to characterizing teleparallel geometries is to compute scalar polynomial invariants constructed from the torsion tensor and its covariant derivatives. An open question has been whether the set of all scalar polynomial torsion invariants, , uniquely characterize a given teleparallel geometry. In this paper, we show that the answer is no and construct the most general class of teleparallel geometries in four dimensions, which cannot be characterized by . As a corollary, we determine all teleparallel geometries, have vanishing scalar polynomial torsion invariants.
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Research Article|
May 13 2021
Teleparallel geometries not characterized by their scalar polynomial torsion invariants
D. D. McNutt
;
D. D. McNutt
a)
1
Faculty of Science and Technology, University of Stavanger
, N-4036 Stavanger, Norway
a)Author to whom correspondence should be addressed: [email protected]
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A. A. Coley
;
A. A. Coley
b)
2
Department of Mathematics and Statistics, Dalhousie University
, Halifax, Nova Scotia B3H 3J5, Canada
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R. J. van den Hoogen
R. J. van den Hoogen
c)
3
Department of Mathematics and Statistics, St. Francis Xavier University
, Antigonish, Nova Scotia B2G 2W5, Canada
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a)Author to whom correspondence should be addressed: [email protected]
J. Math. Phys. 62, 052501 (2021)
Article history
Received:
March 25 2021
Accepted:
April 26 2021
Citation
D. D. McNutt, A. A. Coley, R. J. van den Hoogen; Teleparallel geometries not characterized by their scalar polynomial torsion invariants. J. Math. Phys. 1 May 2021; 62 (5): 052501. https://doi.org/10.1063/5.0051400
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