ON ISOMETRIC IMMERSIONS OF A RIEMANNIAN SPACE WITH LITTLE REGULARITY
2004 ◽
Vol 02
(03)
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pp. 193-226
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Keyword(s):
We consider a Riemannian metric in an open subset of the d-dimensional Euclidean space and assume that its Riemann curvature tensor vanishes. If the metric is of class C2, a classical theorem in differential geometry asserts that the Riemannian space is locally isometrically immersed in the d-dimensional Euclidean space. We establish that if the metric belongs to the Sobolev space W1,∞ and its Riemann curvature tensor vanishes in the space of distributions, then the Riemannian space is still locally isometrically immersed in the d-dimensional Euclidean space.
1984 ◽
Vol 23
(10)
◽
pp. 1001-1008
2009 ◽
Vol 52
(3)
◽
pp. 361-365
◽
Keyword(s):
2016 ◽
Vol 25
(10)
◽
pp. 1650055
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2021 ◽
2018 ◽
1988 ◽
Vol 5
(5)
◽
pp. 695-705
◽