Document Type

Book

Publication Date

1-2017

Abstract

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.

Comments

© 2017 The Author(s). Licensee IntechOpen.

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Publication Title

Manifolds - Current Research Areas

DOI

10.5772/67008

Included in

Mathematics Commons

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