KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS

KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS

KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS

KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS

KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS

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doi:10.1007/s10473-025-0112-z

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 153-160.doi: 10.1007/s10473-025-0112-z

Ralph Howard

Department of Mathematics, University of South Carolina, Columbia, S.C. 29208, USA

收稿日期:2024-08-30 发布日期:2025-02-06
作者简介:Ralph Howard, E-mail,: howard@math.sc.edu

Ralph Howard

Department of Mathematics, University of South Carolina, Columbia, S.C. 29208, USA

Received:2024-08-30 Published:2025-02-06
About author:Ralph Howard, E-mail,: howard@math.sc.edu

摘要： Let $G_q\mathbb{R}^{n})$ be the Grassmannian of all linear $q$ dimensional subspaces of $\mathbb{R}^{n}$ and $I$ an integral invariant of $p+q-n$ dimensional submanifolds of $\mathbb{R}^{n}$ . Then we give methods of evaluating Crofton type integral $\int_{G_q(\mathbb{R}^{n})} I(M\cap L)\,{\rm d}L.$ The methods also work for various generalizations of $G_q(\mathbb{R}^{n})$ such as complex Grassmannians.

关键词: Kinematic formulas, Crofton formulas

Abstract: Let $G_q\mathbb{R}^{n})$ be the Grassmannian of all linear $q$ dimensional subspaces of $\mathbb{R}^{n}$ and $I$ an integral invariant of $p+q-n$ dimensional submanifolds of $\mathbb{R}^{n}$ . Then we give methods of evaluating Crofton type integral $\int_{G_q(\mathbb{R}^{n})} I(M\cap L)\,{\rm d}L.$ The methods also work for various generalizations of $G_q(\mathbb{R}^{n})$ such as complex Grassmannians.

Key words: Kinematic formulas, Crofton formulas

中图分类号:

53C65

Ralph Howard. KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS[J]. 数学物理学报(英文版), 2025, 45(1): 153-160.

Ralph Howard. KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS[J]. Acta mathematica scientia,Series B, 2025, 45(1): 153-160.

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