Pith. Sign in

RECORD

Isospectral deformations of closed Riemannian manifolds with different scalar curvature

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David. L. Webb, Edward N. Wilson

dg-ga · Submitted 6 Oct 1997

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

The authors' main claim We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDdg-ga/9710004 (version 1)
Pith ID3FMLKVY7, Pith's permanent record of this paper and its review
CitationCarolyn S. Gordon, David. L. Webb, Dorothee Schueth, Edward N. Wilson, Ruth Gornet. "Isospectral deformations of closed Riemannian manifolds with different scalar curvature." arXiv:dg-ga/9710004 (1997). https://pith.science/paper/3FMLKVY7
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,019 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.38 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

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 construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. contribution 0.84 0.96 0.83 asserted 1.00
s1 These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. result 0.91 0.87 0.13 asserted 1.00
s2 For some of the deformations, the maximum scalar curvature changes during the deformation. result 0.99 0.92 0.14 asserted 0.91

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

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.