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Mar 9, 2023 at 19:33 comment added TK-421 Gladly! I hope it proves helpful despite being a short section in the book. That's the only reference I know for commuting Hessians off the top of my head. It won't answer your interest in extension problems, but perhaps the additional references will lead you to relevant literature.
Mar 8, 2023 at 15:30 comment added Robert Young Thanks! The equation seemed nice enough that I figured there must be some work on it, but my searches didn't turn up anything. I'll grab a copy of Ivey and Landsberg from the library.
Mar 7, 2023 at 21:59 comment added TK-421 Section 6.9 of the 2nd edition of Cartan for Beginners by Ivey and Landsberg has a discussion of (and additional refernces for) the problem of commuting hessians.
Mar 7, 2023 at 21:09 history asked Robert Young CC BY-SA 4.0