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Projectively flat Finsler 2-spheres of constant curvature

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Robert L. Bryant

dg-ga · Submitted 25 Nov 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is homogeneous or symmetric, namely the Riemannian one.

how it is stated · asserted 1.00 read the record →

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arXiv IDdg-ga/9611010 (version 1)
Pith ID42ZR2RHW, Pith's permanent record of this paper and its review
CitationRobert L. Bryant. "Projectively flat Finsler 2-spheres of constant curvature." arXiv:dg-ga/9611010 (1996). https://pith.science/paper/42ZR2RHW
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,945 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.46 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is homogeneous or symmetric, namely the Riemannian one. I discuss the history of the problem and its relation with Hilbert's Fourth Problem and the calculus of variations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. contribution 0.96 0.94 0.19 asserted 0.99
s1 Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is homogeneous or symmetric, namely the Riemannian one. result 1.00 0.88 0.82 asserted 1.00
s2 I discuss the history of the problem and its relation with Hilbert's Fourth Problem and the calculus of variations. background 0.95 0.38 0.02 asserted 0.87

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is homogeneous or symmetric, namely the Riemannian one. I discuss the history of the problem and its relation with Hilbert's Fourth Problem and the calculus of variations.

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