Taiwanese Journal of Mathematics

On the Kinematic Formula of the Total Mean Curvature Matrix

Chunna Zeng, Lei Ma, and Yin Tong

Full-text: Open access

Abstract

In an earlier paper [23] the authors introduced a new ellipsoid associated with a submanifold, and established an integral formula for the total mean curvature matrix of hypersurfaces. In the present paper a kinematic formula for the total mean curvature matrix of submanifolds in $\mathbb{R}^{n}$ is proved.

Article information

Source
Taiwanese J. Math., Volume 21, Number 1 (2017), 43-54.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874556

Digital Object Identifier
doi:10.11650/tjm.21.2017.7740

Mathematical Reviews number (MathSciNet)
MR3613973

Zentralblatt MATH identifier
1375.53021

Subjects
Primary: 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
Secondary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]

Keywords
LYZ ellipsoid mean curvature vector total mean curvature matrix kinematic formula

Citation

Zeng, Chunna; Ma, Lei; Tong, Yin. On the Kinematic Formula of the Total Mean Curvature Matrix. Taiwanese J. Math. 21 (2017), no. 1, 43--54. doi:10.11650/tjm.21.2017.7740. https://projecteuclid.org/euclid.twjm/1498874556


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