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February 2001 On the areas of geodesic triangles on a surface
Eiji KANEDA, Kazuhiro KISO
Hokkaido Math. J. 30(1): 195-204 (February 2001). DOI: 10.14492/hokmj/1350911931

Abstract

This paper treats geodesic triangles on two-dimensional orientable Riemannian manifolds $M$. Fixing two vertices $A$ and $B$, we can consider the area and the interior angles of the geodesic triangle $\Delta PAB$ as smooth functions of $P$. Applying the Laplace operator to these functions, we obtain formulas for the area and interior angles of $\Delta APAB$. It is shown that if $M$ is of constant curvature, the area and interior angles of geodesic triangles are harmonic.

Citation

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Eiji KANEDA. Kazuhiro KISO. "On the areas of geodesic triangles on a surface." Hokkaido Math. J. 30 (1) 195 - 204, February 2001. https://doi.org/10.14492/hokmj/1350911931

Information

Published: February 2001
First available in Project Euclid: 22 October 2012

zbMATH: 1007.53016
MathSciNet: MR1815888
Digital Object Identifier: 10.14492/hokmj/1350911931

Subjects:
Primary: 53B20
Secondary: 26B20, 53C22

Rights: Copyright © 2001 Hokkaido University, Department of Mathematics

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Vol.30 • No. 1 • February 2001
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