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Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric

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Martha P. Dussan, Nikos Georgiou, Martin Magid

Differential Geometry · Submitted 12 Mar 2016

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

The authors' main claim We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations.

how it is stated · asserted 1.00 read the record →

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arXiv ID1603.03877 (version 1)
Pith IDLNAAWZU3, Pith's permanent record of this paper and its review
CitationMartha P. Dussan, Martin Magid, Nikos Georgiou. "Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric." arXiv:1603.03877 (2016). https://pith.science/paper/LNAAWZU3
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,592 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. Finally, in some cases we give a topological classification of compact minimal surfaces.

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 investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. contribution 0.93 0.89 0.07 asserted 0.96
s1 Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere. background 0.97 0.16 0.02 asserted 0.98
s2 We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. result 0.64 0.96 0.34 asserted 1.00
s3 Finally, in some cases we give a topological classification of compact minimal surfaces. result 0.79 0.95 0.20 asserted 0.84

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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  • full text
  • figures and tables
  • references and citing sentences
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  • P abstract
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  • 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

We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. Finally, in some cases we give a topological classification of compact minimal surfaces.

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