In this paper, we have proved that a projectively flat Sasakian manifold is an Einstein manifold. Also, if an Einstein-Sasakian manifold is projectively flat, then it is locally isometric with a unit sphere S(1). It has also been proved that if in an Einsten-Sasakian manifold the relation K(X, Y ).P = 0 holds, then it is locally isometric with a unit sphere S(1). AMS Mathematics Subject Classif...

We study a class of two-dimensional Finsler metrics defined by a Riemannian metric α and a 1-form β. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact that β is always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of t...

We construct infinitely many two-dimensional Finsler metrics on S 2 and D 2 with non-zero constant flag curvature. They are all not locally projectively flat.

We study the cylindrical symmetric Finsler metrics. obtain system of differential equations such metrics which are projectively flat. give a family solutions this system. Examples included.