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Volume 21, Issue 5
Curvature Computations of 2-Manifolds in $\mathbb{R}^k$

Guo-Liang Xu & Chandrajit L. Bajaj

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.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-681, author = {Xu , Guo-Liang and Bajaj , Chandrajit L.}, title = {Curvature Computations of 2-Manifolds in $\mathbb{R}^k$}, 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 $\mathbb{R}^k$ AU - Xu , Guo-Liang AU - Bajaj , Chandrajit L. 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, Mean curvature vector, Principal curvatures, 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 $k\geq3$.

Guo-Liang Xu & Chandrajit L. Bajaj. (1970). Curvature Computations of 2-Manifolds in $\mathbb{R}^k$. Journal of Computational Mathematics. 21 (5). 681-688. doi:
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