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On phi-Recurrent (k, m)-Contact Metric Manifolds

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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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E. Peyghan, A. Tayebi

Differential Geometry · Submitted 16 Feb 2013

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

The authors' main claim In this paper, we show that there is no phi-recurrent Sasakian manifold.

how it is stated · asserted 1.00 read the record →

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arXiv ID1302.4429 (version 1)
Pith ID6DEZMGDS, Pith's permanent record of this paper and its review
CitationA. Tayebi, E. Peyghan. "On phi-Recurrent (k, m)-Contact Metric Manifolds." arXiv:1302.4429 (2013). https://pith.science/paper/6DEZMGDS
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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, 2,224 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.27 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.38 · compares with prior results 0.10 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we show that there is no phi-recurrent Sasakian manifold. Then we prove that the only flat 3-dimensional manifolds are phi-recurrent (k, m)-contact metric manifolds.

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 In this paper, we show that there is no phi-recurrent Sasakian manifold. result 0.99 0.94 0.46 asserted 1.00
s1 Then we prove that the only flat 3-dimensional manifolds are phi-recurrent (k, m)-contact metric manifolds. result 0.99 0.93 0.36 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

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

In this paper, we show that there is no phi-recurrent Sasakian manifold. Then we prove that the only flat 3-dimensional manifolds are phi-recurrent (k, m)-contact metric manifolds.

Human review

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