In this study, we search slant submanifolds of almost product semi-Riemannian manifold. Accordingly, we investigate slant submanifolds of semi-Riemannian manifold by making the classifications as slant Riemannian, slant semi-Riemannian and slant lightlike submanifold. Moreover, we add the theorems which characterize existence of slant submanifold.

In this study, we worked on the second kind of relaxed elastic lines on dual spaces which has an important point on kinematic. We also obtained boundary conditions for this type of curves. Moreover, the minimization problem of the energy which occurs with an applied force on an elastic line was discussed. Then, we researched the formed potential energy due to the applied force and derived boundary conditions for that case.