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Linear transports along paths in vector bundles V. Properties of curvature and torsion

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Bozhidar Z. Iliev (Institute for Nuclear Research, Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria)

dg-ga · Submitted 20 Sep 1997

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

The authors' main claim The obtained results contain as special cases the corresponding classical ones concerning curvature and torsion of linear connections.

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arXiv IDdg-ga/9709017 (version 2)
Pith IDAG52F426, Pith's permanent record of this paper and its review
CitationBozhidar Z. Iliev (Institute for Nuclear Research, Bulgaria), Bulgarian Academy of Sciences, Nuclear Energy, Sofia. "Linear transports along paths in vector bundles V. Properties of curvature and torsion." arXiv:dg-ga/9709017 (1997). https://pith.science/paper/AG52F426
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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, 2,817 input tokens, $0.0001 reported.

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 0.10 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the corresponding classical ones concerning curvature and torsion of linear connections.

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 geometric interpretation of curvature and torsion of linear transports along paths is presented. contribution 0.93 0.89 0.36 asserted 1.00
s1 A number of (Bianchi type) identities satisfied by these quantities are derived. result 0.83 0.95 0.17 asserted 1.00
s2 The obtained results contain as special cases the corresponding classical ones concerning curvature and torsion of linear connections. interpretation 0.61 0.81 0.24 asserted 1.00

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

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
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  • T body sentences
  • C citations
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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

A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the corresponding classical ones concerning curvature and torsion of linear connections.

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