Schur-type Theorems about Angles and Heights

Xiao Le SU, Yi TAN, Yu Sheng WANG

Acta Mathematica Sinica, Chinese Series ›› 2023, Vol. 66 ›› Issue (2) : 199-208.

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Acta Mathematica Sinica, Chinese Series ›› 2023, Vol. 66 ›› Issue (2) : 199-208. DOI: 10.12386/A20210060

Schur-type Theorems about Angles and Heights

  • Xiao Le SU, Yi TAN, Yu Sheng WANG
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Abstract

In differential geometry, there is a classical result, named Schur's Theorem, which is about the comparison of chords of two curves in E3. Inspired by it, this paper presents Schur-type theorems about the comparison of chord tangent angles of two curves, and the comparison of heights of two curves relative to their chords.

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Schur’s Theorem / curvature / convex curve / chord tangent angle / congruent

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Xiao Le SU, Yi TAN, Yu Sheng WANG. Schur-type Theorems about Angles and Heights. Acta Mathematica Sinica, Chinese Series, 2023, 66(2): 199-208 https://doi.org/10.12386/A20210060

References

[1] Hopf H., Differential Geometry in the Large, Springer-Verlag, Berlin, 1983.
[2] Shen Y. B., Global Differential Geometry (in Chinese), Higher Education Press, Beijing, 2009.
[3] Sullivan John M., Curves of finite total curvature, In:Discrete Differential Geometry, Oberwolfach Seminars, Basel:Birkhäuser, Vol. 38, 2008.
[4] Wang Y. N., Liu J. Z., Lecture on Differential Geometry (2nd Ed.) (in Chinese), Beijing Normal University Press, Beijing, 2011.
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