Affine analogues of the Sasaki-Shchepetilov connection
2016 ◽
Vol 15
(1)
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pp. 37-49
Keyword(s):
AbstractFor two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM ⊕ E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections on TM ⊕ (ℝ × M) and two on TM ⊕ (ℝ2 × M) are constructed. It is shown that two of those connections – one from each pair – may be identified with the standard flat connection in ℝN, after suitable local affine embedding of (M,∇) into ℝN.
2014 ◽
Vol 13
(1)
◽
pp. 19-43
2019 ◽
Vol 16
(06)
◽
pp. 1840025
2019 ◽
Vol 59
◽
pp. 394-405
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Keyword(s):
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2013 ◽
Vol 2013
◽
pp. 1-7
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1997 ◽
Vol 11
(26n27)
◽
pp. 3195-3206
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Keyword(s):