Advanced Studies in Pure Mathematics

Riemann-Finsler surfaces

Sorin V. Sabau and Hideo Shimada

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Abstract

This paper study the Gauss-Bonnet theorem for Finsler surfaces with smooth boundary. This is a natural generalization of the Gauss-Bonnet theorem for Riemannian surfaces with smooth boundary as well as an extension of the Gauss-Bonnet theorem for boundaryless Finsler surfaces. The paper starts with an introduction in the Finsler geometry of surfaces with emphasis on the Berwald and Landsberg surfaces.

Article information

Source
Finsler Geometry, Sapporo 2005 — In Memory of Makoto Matsumoto, S. V. Sabau and H. Shimada, eds. (Tokyo: Mathematical Society of Japan, 2007), 125-162

Dates
Received: 1 September 2006
Revised: 13 March 2007
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1545001105

Digital Object Identifier
doi:10.2969/aspm/04810125

Mathematical Reviews number (MathSciNet)
MR2389254

Zentralblatt MATH identifier
1144.53093

Subjects
Primary: 53B40: Finsler spaces and generalizations (areal metrics) 53C60: Finsler spaces and generalizations (areal metrics) [See also 58B20]

Keywords
Gauss-Bonnet theorem Minkowski planes Berwald metrics Landsberg metrics

Citation

Sabau, Sorin V.; Shimada, Hideo. Riemann-Finsler surfaces. Finsler Geometry, Sapporo 2005 — In Memory of Makoto Matsumoto, 125--162, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04810125. https://projecteuclid.org/euclid.aspm/1545001105


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