Return to Question

Let $M$ be a sub-Riemannian space. Consider a smooth curve $\gamma:[0,1]\to M$ such that $\dot\gamma(t)\not\in H_{\gamma(t)}$, where $H_{\gamma(t)}$ is the horizontal subbundle ( i.e. $\gamma$ is totally non-horizontal curve).

Is it obvious that the curve is not rectifiable or has infinite length? I haven't found any mentions about this questions.

Let $M$ be a sub-Riemannian space. Consider a smooth curve $\gamma:[0,1]\to M$ such that $\dot\gamma(t)\not\in H_{\gamma(t)}$, where $H_{\gamma(t)}$ is the horizontal subbundle ( i.e. $\gamma$ is totally non-horizontal curve).

Is it obvious that the curve is not rectifiable or has infinite length?

Let $M$ be a sub-Riemannian space. Consider a curve $\gamma:[0,1]\to M$ such that $\dot\gamma(t)\not\in TM_{\gamma(t)}$ (totally non-horizontal curve).

Is it obvious that the curve is not rectifiable or has infinite length? I haven't found any mentions about this questions.

Let $M$ be a sub-Riemannian space. Consider a smooth curve $\gamma:[0,1]\to M$ such that $\dot\gamma(t)\not\in H_{\gamma(t)}$, where $H_{\gamma(t)}$ is the horizontal subbundle ( i.e. $\gamma$ is totally non-horizontal curve).

Is it obvious that the curve is not rectifiable or has infinite length? I haven't found any mentions about this questions.

Let $M$ - sub-Riemannian space. A curve $\gamma:[0,1]\to M$ such that $\dot\gamma(t)\not\in TM_{\gamma(t)}$ ( totally non horizontal curve  ).

Is it obvious that the curve is not rectifiable or has infinite length? I haven't found any mentions about this questions.

Let $M$ be a sub-Riemannian space. Consider a curve $\gamma:[0,1]\to M$ such that $\dot\gamma(t)\not\in TM_{\gamma(t)}$ (totally non-horizontal curve).

Is it obvious that the curve is not rectifiable or has infinite length? I haven't found any mentions about this questions.