Variation of Gaussian Curvature under Conformal Mapping and its Application

Authors

Matthew He, Nova Southeastern UniversityFollow
Dmitry B. Goldgof, University of South Florida
Chandra Kambhamettu, University of South Florida

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.

NSUWorks Citation

He, Matthew; Goldgof, Dmitry B.; and Kambhamettu, Chandra, "Variation of Gaussian Curvature under Conformal Mapping and its Application" (1993). Mathematics Faculty Articles. 175.
https://nsuworks.nova.edu/math_facarticles/175

DOI

10.1016/0898-1221(93)90086-B