‎On projectively PR-flat Douglas sprays

Deformation of every spray into a projective spray can be done using a volume form on a manifold. The Riemann curvature of a projective spray is called the projective Riemmann curvature. In this paper, we present a global rigidity result for projectively PR-flat sprays that have vanishing Douglas curvature. Then we study and characterize projectively PR-flat Randers metrics of Douglas curvature‎.

کلیدواژه ها:

Sprays ، projective Riemann curvature ، Douglas ‎curvature