  Let $M=SO(1,4)/SO(1,3)\simeq S^{3}\times\mathbb{R}$ (a parallelizable
manifold) be a submanifold in the structure $(\mathring{M}%
,\boldsymbol{\mathring{g}})$ (hereafter called the bulk) where $\mathring
{M}\simeq\mathbb{R}^{5}$ and $\boldsymbol{\mathring{g}}$ is a pseudo Euclidian
metric of signature $(1,4)$. Let $\boldsymbol{i}:M\rightarrow\mathbb{R}^{5}$ be
the inclusion map and let \ $\boldsymbol{g}=\boldsymbol{i}^{\ast
}\boldsymbol{\mathring{g}}$ be the pullback metric on $M$. It has signature
$(1,3)$ Let $\boldsymbol{D}$ be the Levi-Civita connection of $\boldsymbol{g}%
$. We call the structure $(M,\boldsymbol{g})$ a de Sitter manifold and
$M^{dSL}=(M=\mathbb{R\times}S^{3},\boldsymbol{g},\boldsymbol{D},\tau
_{\boldsymbol{g}},\uparrow)$ a de Sitter spacetime structure, which is \ of
course orientable by $\tau_{\boldsymbol{g}}\in\sec% %TCIMACRO{\tbigwedge
\nolimits^{4}}% %BeginExpansion {\textstyle\bigwedge\nolimits^{4}}
%EndExpansion T^{\ast}M$ and time orientable (by $\uparrow$).\ Under these
conditions we prove that if the motion of a free particle moving on $M$ happens
with constant \emph{bulk} angular momentum then its motion in the structure
$M^{dSL}$ is a timelike geodesic. Also any geodesic motion in the structure
$M^{dSL}$ implies that the particle has constant angular momentum in the bulk.
