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Supplement on Curved flats in the space of point pairs and Isothermic surfaces: A Quaternionic Calculus

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Udo Hertrich-Jeromin

dg-ga · Submitted 24 Sep 1997

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

The authors' main claim A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented --- in particular, a new form of Bryant's Weierstrass type representation for surfaces of constant mean curvature 1 in hyperbolic 3-space is given.

how it is stated · asserted 1.00 read the record →

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arXiv IDdg-ga/9709019 (version 1)
Pith IDE2GHOB5I, Pith's permanent record of this paper and its review
CitationUdo Hertrich-Jeromin. "Supplement on Curved flats in the space of point pairs and Isothermic surfaces: A Quaternionic Calculus." arXiv:dg-ga/9709019 (1997). https://pith.science/paper/E2GHOB5I
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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, 2,995 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.41 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented --- in particular, a new form of Bryant's Weierstrass type representation for surfaces of constant mean curvature 1 in hyperbolic 3-space is given.

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 A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. contribution 0.71 0.91 0.10 asserted 1.00
s1 This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. contribution 0.74 0.83 0.24 asserted 0.99
s2 A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented --- in particular, a new form of Bryant's Weierstrass type representation for surfaces of constant mean curvature 1 in hyperbolic 3-space is given. contribution 0.84 0.91 0.38 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.90 · 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

A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented --- in particular, a new form of Bryant's Weierstrass type representation for surfaces of constant mean curvature 1 in hyperbolic 3-space is given.

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