In this study,we have considered the rotational motions of a particle around the origin of the unit 2-sphere $S_2^2$ with constant angular velocity in semi-Euclidean 3-spacewithindextwo $E^3_2$, namely geodesic motions of $SO(2,1)$. Then we have obtained the vector and the matrix representations of the spherical rotations around the origin of a particle on $S_2^2$. Furthermore, we consider some relations between semi-Riemann spaces $SO(2,1)$ and $T_1S_2^2$ such as diffeomorphism and isometry. We have obtained the system of differential equations giving geodesics of Sasaki semi-Riemann manifold $(T_1S_2^2,g^S)$ . Moreover, we consider the stationary motion of a particle on $S_2^2$ corresponding to one parameter curve of $SO(2,1)$, which determines a geodesic of $SO(2,1)$. Finally, we obtain the system of differential equations giving geodesics of the semi-Riemann space $(SO(2,1),h)$ and we show that the system of differential equations giving geodesics of Riemann space $(SO(2,1),h)$ is equal to that of $(T_1S_2 2,g^S)$.
Tangent sphere bundle, rotational group in semi-Euclidean 3-space, geodesics
"Geodesic motions in SO(2,1),"
Turkish Journal of Mathematics: Vol. 44:
2, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss2/17