Variation of Gaussian Curvature under Conformal Mapping and its Application
Computers & Mathematics with Applications
Conformal mapping, Gaussian curvature, Non-rigid motion, Differential geometry
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.
He, Matthew; Goldgof, Dmitry B.; and Kambhamettu, Chandra, "Variation of Gaussian Curvature under Conformal Mapping and its Application" (1993). Mathematics Faculty Articles. 175.