Conditions for the local existence of metric in a generic affine manifold
1980 ◽
Vol 87
(3)
◽
pp. 527-534
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Keyword(s):
AbstractFor a manifold with a generic symmetric affine connection, explicit necessary and sufficient conditions for the local existence of metric compatible with the connection are obtained in terms of the Riemann tensor and its first-order covariant derivatives. If these conditions are satisfied, the solutions for metric are unique up to a constant scale factor and the absolute value of the signature is uniquely determined. Explicit formulae for the solutions are given in terms of integrals.
1981 ◽
Vol 90
(3)
◽
pp. 517-527
◽
2008 ◽
Vol 55
(6)
◽
pp. 1279-1292
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1977 ◽
Vol 99
(2)
◽
pp. 85-90
◽
2006 ◽
Vol 321
(2)
◽
pp. 553-568
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2018 ◽
Vol 2018
◽
pp. 1-8