Volume 21, Issue 5
Curvature Computations of 2-Manifolds in Rk
DOI:

J. Comp. Math., 21 (2003), pp. 681-688

Published online: 2003-10

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• Abstract

In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in $R^k$ with $k\geq3$.

• Keywords

Riemannian curvature Mean curvature vector Principal curvatures Principal directions

@Article{JCM-21-681, author = {Guo-liang Xu and Chandrajit L. Bajaj}, title = {Curvature Computations of 2-Manifolds in Rk}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {5}, pages = {681--688}, abstract = { In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in $R^k$ with $k\geq3$. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10246.html} }
TY - JOUR T1 - Curvature Computations of 2-Manifolds in Rk AU - Guo-liang Xu & Chandrajit L. Bajaj JO - Journal of Computational Mathematics VL - 5 SP - 681 EP - 688 PY - 2003 DA - 2003/10 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10246.html KW - Riemannian curvature KW - Mean curvature vector KW - Principal curvatures KW - Principal directions AB - In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in $R^k$ with $k\geq3$.