Tangent map of the inclusion map of a submanifold

Question

Let $M$ be the Minkowski spacetime, let $f\in C^{\infty}(M)$ be defined as $f(m)=x^{0}(m)$, with $\{x^{\mu}\}$ being a global Cartesian coordinates system, and let $M\supset F_{t}=f^{-1}(t)$ be the submanifold relative to a regular value $t\in\mathbb{R}$ of $f$. How can the inclusion map $\iota_{t}:F_{t}\longrightarrow M$ and the tangent map $T\iota_{t}:TF_{t}\longrightarrow TM$ be visualized?

Answer 1

The inclusion map is given by the identity (if you see $F_t$ as a subspace of $M$), the tangent map $T\iota$ is the inclusion of the tangent space of $F_t$ in $TM$