Hamel functions and Funk functions of a spray are generalization of locally projectively flat Finsler metrics and Funk metrics respectively. In this paper, we study sprays on Hamel or Funk functions model. We use the ...Hamel functions and Funk functions of a spray are generalization of locally projectively flat Finsler metrics and Funk metrics respectively. In this paper, we study sprays on Hamel or Funk functions model. We use the Funk metric to construct a family of sprays and obtain some of their curvature properties and metrizability conditions. We prove that there exist local Funk functions on a R-flat spray manifold. On certain projectively flat Berwald spray manifolds, we construct a multitude of nonzero Funk functions. We introduce a new class of sprays called Hamel or Funk sprays associated to given sprays and Hamel or Funk functions, and then obtain some special properties of a Hamel or Funk spray of scalar curvature, especially on its metrizability and the special form of its Riemann curvature.展开更多
文摘Hamel functions and Funk functions of a spray are generalization of locally projectively flat Finsler metrics and Funk metrics respectively. In this paper, we study sprays on Hamel or Funk functions model. We use the Funk metric to construct a family of sprays and obtain some of their curvature properties and metrizability conditions. We prove that there exist local Funk functions on a R-flat spray manifold. On certain projectively flat Berwald spray manifolds, we construct a multitude of nonzero Funk functions. We introduce a new class of sprays called Hamel or Funk sprays associated to given sprays and Hamel or Funk functions, and then obtain some special properties of a Hamel or Funk spray of scalar curvature, especially on its metrizability and the special form of its Riemann curvature.
