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Hyper-symplectic structures on integrable systems

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C. Bartocci, I. Mencattini

Differential Geometry · Submitted 26 Aug 2003

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

The authors' main claim We prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure.

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arXiv IDmath/0308244 (version 1)
Pith ID3FC5APZA, Pith's permanent record of this paper and its review
CitationC. Bartocci, I. Mencattini. "Hyper-symplectic structures on integrable systems." arXiv:math/0308244 (2003). https://pith.science/paper/3FC5APZA
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,277 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure. Moreover, a special Kaehler structure is induced on the base manifold.

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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 prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure. result 0.91 0.93 0.89 asserted 1.00
s1 Moreover, a special Kaehler structure is induced on the base manifold. result 1.00 0.79 0.10 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

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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 prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure. Moreover, a special Kaehler structure is induced on the base manifold.

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