An Intrinsic Characterization of Bonnet Surfaces Based on a Closed Differential Ideal
Keyword(s):
The structure equations for a two-dimensional manifold are introduced and two results based on the Codazzi equations pertinent to the study of isometric surfaces are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem due to Bonnet is obtained. A transformation for the connection forms is developed. It is proved that the angle of deformation must be harmonic, and that the differentials of many of the important variables generate a closed differential ideal. This implies that a coordinate system exists in which many of the variables satisfy particular ordinary differential equations, and these results can be used to characterize Bonnet surfaces.
1970 ◽
Vol 10
(1)
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pp. 95-111
Keyword(s):
Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials
2013 ◽
Vol 5
(2)
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pp. 212-221
1999 ◽
Vol 14
(37)
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pp. 2595-2604
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2007 ◽
Vol 40
(1)
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pp. 6-26
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1997 ◽
Vol 206
(2)
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pp. 364-388
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