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nLab > Latest Changes: quaternionic manifold

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  1.  
    • CommentRowNumber1.
    • CommentAuthorJames Francese
    • CommentTimeMar 20th 2019

    I’ve created a page for quaternionic manifolds, linked from quaternion-Kähler page. Basic references and discussion of main definition re Cauchy-Feuter calculus. Comparison to hypercomplex structure.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 21st 2019

    Thanks! And I have added now the link going the other way, too.

    Might you have energy to add a sentence putting the two in relation?

    • CommentRowNumber3.
    • CommentAuthorJames Francese
    • CommentTimeMar 21st 2019

    Great idea, I’ve added a comment connecting their notations and a statement of why quaternionic-Kähler manifolds are indeed quaternionic.

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 21st 2019
    • (edited Mar 21st 2019)

    Thanks!

    I gave the discussion of “qK is q” a numbered Example-environment (here) and placed that inside an Examples section.

    Also, I created a Properties-section and made your two stub sections “Holonomy” and “Twistor space” be subsections of that.

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 21st 2019
    • (edited Mar 21st 2019)

    By the way, I would tend to make your “Discussion”-subsection be a numbered Remark inside the “Definition”-section instead.

    (I find it helpful to think in terms of textbook organization: There we would rarely make a comment on a definition be its own subsection.)

    • CommentRowNumber6.
    • CommentAuthorJames Francese
    • CommentTimeMar 21st 2019

    Thanks Urs. And agreed, that is much more natural. I’m paying attention to the changes you’ve been making as I add material; as I learn more itex + markdown and nLab style I can follow suit.

    • CommentRowNumber7.
    • CommentAuthorJames Francese
    • CommentTimeMar 21st 2019

    Added more classical and a few specialty references, including Bonan’s seminal paper.

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 15th 2020
    • (edited Jul 15th 2020)

    completed the pointer to

    • Dmitri V. Alekseevsky, Stefano Marchiafava, Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions, Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993) Volume: 4, Issue: 1, page 43-52 (dml:244082)

    and added pointer to

    • Dmitri V. Alekseevsky, Stefano Marchiafava, Quaternionic-like structures on a manifold: Note II. Automorphism groups and their interrelations, Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993) Volume: 4, Issue: 1, page 53-61 (dml:244299)

    diff, v8, current

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