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Reduced Vectorial Ribaucour Transformation for the Darboux-Egoroff Equations

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Q. P. Liu, M. Manas

solv-int · Submitted 11 May 1998

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

The authors' main claim This is combined with the orthogonal reduction of Lame type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction.

how it is stated · asserted 1.00 read the record →

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arXiv IDsolv-int/9805005 (version 1)
Pith IDH37XQUX3, Pith's permanent record of this paper and its review
CitationM. Manas, Q. P. Liu. "Reduced Vectorial Ribaucour Transformation for the Darboux-Egoroff Equations." arXiv:solv-int/9805005 (1998). https://pith.science/paper/H37XQUX3
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,479 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lame type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transformations. Finally, as an example, we apply these transformations to the Cartesian background.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. contribution 0.81 0.83 0.27 asserted 1.00
s1 This is combined with the orthogonal reduction of Lame type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. method 0.59 0.87 0.32 asserted 1.00
s2 We also show that a permutability property holds for all these transformations. result 0.94 0.94 0.21 asserted 1.00
s3 Finally, as an example, we apply these transformations to the Cartesian background. contribution 0.69 0.93 0.07 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 1.00.

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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

The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lame type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transformations. Finally, as an example, we apply these transformations to the Cartesian background.

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