In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci cu...In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z.Shen.The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M^(n) with a volume form dV on M^(n).展开更多
The notion of the Ricci curvature is defined for sprays on a manifold.With a volume form on a manifold,every spray can be deformed to a projective spray.The Ricci curvature of a projective spray is called the projecti...The notion of the Ricci curvature is defined for sprays on a manifold.With a volume form on a manifold,every spray can be deformed to a projective spray.The Ricci curvature of a projective spray is called the projective Ricci curvature.In this paper,we introduce the notion of projectively Ricci-flat sprays.We establish a global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature.Then we study and characterize projectively Ricci-flat Randers metrics.展开更多
In this paper we define the concept of projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds.
文摘In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z.Shen.The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M^(n) with a volume form dV on M^(n).
文摘The notion of the Ricci curvature is defined for sprays on a manifold.With a volume form on a manifold,every spray can be deformed to a projective spray.The Ricci curvature of a projective spray is called the projective Ricci curvature.In this paper,we introduce the notion of projectively Ricci-flat sprays.We establish a global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature.Then we study and characterize projectively Ricci-flat Randers metrics.
文摘In this paper we define the concept of projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds.
