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4 results on '"Lin, Zaifeng"'

1. On Eisenhart's type theorem for sub-Riemannian metrics on step $2$ distributions with $\mathrm{ad}$-surjective Tanaka symbols

Author

Lin, Zaifeng and Zelenko, Igor

Subjects
Mathematics - Differential Geometry, Mathematics - Optimization and Control, 53C17, 58A30, 58E10, 53A15, 37J39, 35N10, 17B70
Abstract

The classical result of Eisenhart states that if a Riemannian metric $g$ admits a Riemannian metric that is not constantly proportional to $g$ and has the same (parameterized) geodesics as $g$ in a neighborhood of a given point, then $g$ is a direct product of two Riemannian metrics in this neighborhood. We introduce a new generic class of step $2$ graded nilpotent Lie algebras, called $\mathrm{ad}$-surjective, and extend the Eisenhart theorem to sub-Riemannian metrics on step 2 distributions with $\mathrm{ad}$-surjective Tanaka symbols. The class of ad-surjective step 2 nilpotent Lie algebras contains a well-known class of algebras of H-type as a very particular case., Comment: some misprints were corrected, especially in indices of Proposition 4.7

Published
2023

2. On Eisenhart’s Type Theorem for Sub-Riemannian Metrics on Step \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ad}$$\end{document} Distributions with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ad}$$\end{document}-Surjective Tanaka Symbols

Author

Lin, Zaifeng and Zelenko, Igor

Published
2024
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3. On Eisenhart's Type Theorem for Sub-Riemannian Metrics on Step Distributions with -Surjective Tanaka Symbols.

Author

Lin, Zaifeng and Zelenko, Igor

Abstract

The classical result of Eisenhart states that, if a Riemannian metric admits a Riemannian metric that is not constantly proportional to and has the same (parameterized) geodesics as in a neighborhood of a given point, then is a direct product of two Riemannian metrics in this neighborhood. We introduce a new generic class of step graded nilpotent Lie algebras, called -surjective, and extend the Eisenhart theorem to sub-Riemannian metrics on step distributions with -surjective Tanaka symbols. The class of ad-surjective step nilpotent Lie algebras contains a well-known class of algebras of H-type as a very particular case. [ABSTRACT FROM AUTHOR]

Published
2024
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