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On Positive Sasakian Geometry

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Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye

Differential Geometry · Submitted 11 Apr 2001

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

The authors' main claim We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature.

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arXiv IDmath/0104126 (version 1)
Pith IDEDEOMUUP, Pith's permanent record of this paper and its review
CitationCharles P. Boyer, Krzysztof Galicki, Michael Nakamaye. "On Positive Sasakian Geometry." arXiv:math/0104126 (2001). https://pith.science/paper/EDEOMUUP
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,048 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.87 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

A Sasakian structure on a manifold is called {\it positive} if its basic first Chern class can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This allows us by example to give a completely independent proof of a result of Sha and Yang [SY] that for every positive integer k the k-fold connected sum of $S^2\times S^3$ admits metrics of positive Ricci curvature.

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 Sasakian structure on a manifold is called {\it positive} if its basic first Chern class can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. background 1.00 0.12 0.03 asserted 0.99
s1 We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. result 0.91 0.96 0.89 asserted 1.00
s2 This allows us by example to give a completely independent proof of a result of Sha and Yang [SY] that for every positive integer k the k-fold connected sum of $S^2\times S^3$ admits metrics of positive Ricci curvature. interpretation 0.63 0.84 0.14 asserted 0.99

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

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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 Sasakian structure on a manifold is called {\it positive} if its basic first Chern class can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This allows us by example to give a completely independent proof of a result of Sha and Yang [SY] that for every positive integer k the k-fold connected sum of $S^2\times S^3$ admits metrics of positive Ricci curvature.

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