Mathematics Faculty Articles

Title

Variation of Gaussian Curvature under Conformal Mapping and its Application

Document Type

Article

Publication Date

7-1-1993

Publication Title

Computers & Mathematics with Applications

Keywords

Conformal mapping, Gaussian curvature, Non-rigid motion, Differential geometry

ISSN

0898-1221

Volume

26

Issue/No.

1

First Page

63

Last Page

74

Abstract

We characterize conformal mapping between two surfaces, S and S∗, based on Gaussian curvature before and after motion. An explicit representation of the Gaussian curvature after conformal mapping is presented in terms of Riemann-Christoffel tensor and Ricci tensor and their derivatives. Based on changes in surface curvature, we are able to estimate the stretching of non-rigid motion during conformal mapping via a polynomial approximation.

DOI

10.1016/0898-1221(93)90086-B

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