The plastic ratio is a fascinating topic that continually generates new ideas. The purpose of this paper is to point out and find some applications of the plastic ratio in the differential manifold. Precisely, we say that an $(1,1)$-tensor field $P$ on a $m$-dimensional Riemannian manifold $(M, g)$ is a plastic structure if it satisfies the equation $ P^3 = P + I $, where $ I $ is the identity. We establish several properties of the plastic structure. Then we show that a plastic structure induces on every invariant submanifold a plastic structure, too.
Plastic ratio, plastic structure, polynomial structure, Riemannian manifold
NEZHAD, AKBAR DEHGHAN and ARAL, ZOHREH
"Some recent results in plastic structure on Riemannian manifold,"
Turkish Journal of Mathematics: Vol. 46:
8, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss8/1