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• 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.

• 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.

• 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.

• 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.

• 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)
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