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$(\alpha,\beta)$-metrics satisfying the $T$-Condition or the $\sigma T$-Condition

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S. G. Elgendi, Laszlo Kozma

Differential Geometry · Submitted 7 Jun 2018

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

The authors' main claim The Finsler metrics of the first class are Berwaldian, the metrics of the second class are almost regular non-Berwaldian Landsberg metrics.

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arXiv ID1806.02620 (version 3)
Pith IDNUF45H2N, Pith's permanent record of this paper and its review
CitationLaszlo Kozma, S. G. Elgendi. "$(\alpha,\beta)$-metrics satisfying the $T$-Condition or the $\sigma T$-Condition." arXiv:1806.02620 (2018). https://pith.science/paper/NUF45H2N
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,668 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.90 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We describe the $(\alpha,\beta)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(\alpha,\beta)$-metrics that satisfy the $\sigma T$-condition $\sigma_hT^h_{ijk}=0$, where $\sigma_h=\frac{\partial \sigma}{\partial x^h}$ and $\sigma$ is a smooth function on $M$. These classes have already been obtained by Z. Shen and G. S. Asanov in a completely different approach. The Finsler metrics of the first class are Berwaldian, the metrics of the second class are almost regular non-Berwaldian Landsberg metrics.

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 We describe the $(\alpha,\beta)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(\alpha,\beta)$-metrics that satisfy the $\sigma T$-condition $\sigma_hT^h_{ijk}=0$, where $\sigma_h=\frac{\partial \sigma}{\partial x^h}$ and $\sigma$ is a smooth function on $M$. contribution 0.95 0.83 0.33 asserted 0.99
s1 These classes have already been obtained by Z. Shen and G. S. background 1.00 0.03 0.05 asserted 1.00
s2 Asanov in a completely different approach. background 1.00 0.03 0.03 asserted 0.86
s3 The Finsler metrics of the first class are Berwaldian, the metrics of the second class are almost regular non-Berwaldian Landsberg metrics. result 0.92 0.43 0.68 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.77.

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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

We describe the $(\alpha,\beta)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(\alpha,\beta)$-metrics that satisfy the $\sigma T$-condition $\sigma_hT^h_{ijk}=0$, where $\sigma_h=\frac{\partial \sigma}{\partial x^h}$ and $\sigma$ is a smooth function on $M$. These classes have already been obtained by Z. Shen and G. S. Asanov in a completely different approach. The Finsler metrics of the first class are Berwaldian, the metrics of the second class are almost regular non-Berwaldian Landsberg metrics.

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