We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy ...

In this paper, we characterize three-dimensional Riemannian manifolds M 3 M 3 admitting Ricci–Yamabe solitons (RYSs). It is proved that if an M 3 M 3 endowed with a semi-symmetric metric ζ ζ ...