Given a Riemann manifold with a Kozul/Affine connection, if you take any subbundle of the tangent bundle there is an induced connection given by applying the ambient Kozul connection and projecting to the subbundle.
What terminologies are there for this induced connection? Is there one standard, or do different people give it different names?
I'm asking for a colleague who would like to use the construction, and to compute with it, so some gentle references might help.
Small comment: I've seen some rather bizarre terminologies for this construction in some papers. My impression is that if there is a standard terminology it maybe is not used very often. I usually just call it "the induced connection" in my own papers.