Let \(X,Y\in \mathfrak{X}(\mathbb{R}^n)\) be smooth vector fields. The Euclidean connection is defined by
\begin{equation*} \bar{\nabla}_XY = X(Y^i)\partial_i. \end{equation*}Links Link to heading
Remark
- The Euclidean connection on \(\mathbb{R}^n\) is the Levi-Civita connection.