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starting something on isometric immersions
— mainly I was trying to track down a reference that would clearly state that orthonormal “adapted” or “Darboux” (co)frames (here) always exist locally for an immersion into a Riemannian manifold.
What I found so far is
Mastrolia, Rigoli & Setti 2012, p. 33, where this is claimed, but just in passing
and
Chen & Giron 2021, Thm. 2.2, where this is stated in the generality of sequences of immersions, which makes it hard to recognize the simple statement behind all the analytic fine-print.
added the observation (here) that the defining property of Darboux co-frames is just what (later) in the super-embedding approach to super -branes is called the “embedding condition”.
added pointer to (1.12-13) in
What is the reference Lee 2018?
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