2

Does anyone know definition of Levi-Civita connection map that defined as $TTM\to TM$.

I would appreciate if you could give a good reference.

Thanks.

C.F.G
  • 8,789

1 Answers1

2

I think what you are thinking of is the connector for a given connection. For a vector bundle $E$, this is denoted by $K: TE \to E$ in Natural Operations in Differential Geometry by Kolar, Michor, and Slovak. This is an amazing textbook by the way; definitely my go-to reference for anything to do with differential geometry.

ಠ_ಠ
  • 11,310