Variation of Gaussian Curvature under Conformal Mapping and its Application

Matthew He; Dmitry B. Goldgof; Chandra Kambhamettu

doi:10.1016/0898-1221(93)90086-B

Variation of Gaussian Curvature under Conformal Mapping and its Application

Matthew He
, Dmitry B. Goldgof
, Chandra Kambhamettu

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	American English
Pages (from-to)	63-74
Journal	Computers & Mathematics with Applications
Volume	26
Issue number	1
DOIs	https://doi.org/10.1016/0898-1221(93)90086-B
State	Published - Jul 1 1993

Keywords

Conformal mapping
Differential geometry
Gaussian curvature
Non-rigid motion

Disciplines

Mathematics

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Cite this

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title = "Variation of Gaussian Curvature under Conformal Mapping and its Application",

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.",

keywords = "Conformal mapping, Differential geometry, Gaussian curvature, Non-rigid motion",

author = "Matthew He and Goldgof, \{Dmitry B.\} and Chandra Kambhamettu",

year = "1993",

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doi = "10.1016/0898-1221(93)90086-B",

language = "American English",

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pages = "63--74",

journal = "Computers \& Mathematics with Applications",

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T1 - Variation of Gaussian Curvature under Conformal Mapping and its Application

AU - He, Matthew

AU - Goldgof, Dmitry B.

AU - Kambhamettu, Chandra

PY - 1993/7/1

Y1 - 1993/7/1

N2 - 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.

AB - 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.

KW - Conformal mapping

KW - Differential geometry

KW - Gaussian curvature

KW - Non-rigid motion

UR - https://nsuworks.nova.edu/math_facarticles/175

U2 - 10.1016/0898-1221(93)90086-B

DO - 10.1016/0898-1221(93)90086-B

M3 - Article

SN - 0898-1221

VL - 26

SP - 63

EP - 74

JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

IS - 1

ER -

Variation of Gaussian Curvature under Conformal Mapping and its Application

Abstract

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