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Let $(M,g)$ be a Riemannian manifold. Let $S_g$ be the corresponding Sasaki metric on $TM$. For every $p\in M,\;V_p\in TM $, is it true and obvious that $0_p$ is the closest point of the zero section to $V_p$?

With some abuse of terminologies a rephrase of the question would be: Is the height of a rigth triangle shorter than its hypotenuse?

Let $(M,g)$ be a Riemannian manifold. Let $S_g$ be the corresponding Sasaki metric on $TM$. For every $p\in M$, $V_p\in T_pM$, is it true and obvious that $0_p$ is the closest point of the zero section to $V_p$?

With some abuse of terminology a rephrase of the question would be: Is the height of a right triangle shorter than its hypotenuse?

Let $(M,g)$ be a Riemannian manifold. Let $S_g$ be the corresponding Sasaki metric on $TM$. For every $V_p\in TM p\in M$, is it true and obvious that $0_p$ is the closest point of the zero section to $V_p$?

With some abuse of terminologies a rephrase of the question would be: Is the height of a rigth triangle shorter than its hypotenuse?

Let $(M,g)$ be a Riemannian manifold. Let $S_g$ be the corresponding Sasaki metric on $TM$. For every $p\in M,\;V_p\in TM $, is it true and obvious that $0_p$ is the closest point of the zero section to $V_p$?

With some abuse of terminologies a rephrase of the question would be: Is the height of a rigth triangle shorter than its hypotenuse?