Curvature computations for n-manifolds in Rn+m and solution to an open problem proposed by R. Goldman

Authors:
Qin Zhang;Guoliang Xu
Affiliations:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China and Department of Basic Courses, Beijing Information Sc ...;LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Computer Aided Geometric Design
Year:
2007

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Curvature formulas for implicit curves and surfaces

Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry

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Abstract

In this paper, simple and explicit formulas for computing mean curvature vector and Gauss-Kronecker curvature for n-manifolds in R^n^+^m are derived. Using these formulas, we solve an open problem, proposed by Ron Goldman, about curvature formulas for implicit surfaces with higher co-dimensions.