Variation of Gaussian Curvature under Conformal Mapping and its Application

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.

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