On Finsler Space with Randers Conformal Change — Main Scalar, Geodesic and Scalar Curvature
On Finsler Space with Randers Conformal Change — Main Scalar, Geodesic and Scalar Curvature
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具有兰德斯保角变化的芬斯勒空间——主标量、测地线和标量曲率
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Anshuman Mishra
中科院分区：
文献类型：
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作者：
H. Shukla;Anshuman Mishra
设Mn是一个n维可微流形，Fn是一个Finsler空间，它具有Mn的一个基本函数L（x，y），（yi = stecxi）.在本文中，我们将兰德斯共形变化定义为其中σ（x）是x的函数，β（x，y）= B i（x）yi是M n上的1-形式。这种变换是更一般的，因为它包括共形，兰德斯和位似变换作为特殊情况。本文通过对Fn的兰德斯共形变换，给出了二维Finsler空间的标量曲率和主标量的表达式。我们还得到了这种变换空间的测地线方程。
: Let M n be an n-dimensional differentiable manifold and F n be a Finsler space equipped with a fundamental function L ( x, y ) , ( y i = ˙ x i ) of M n . In the present paper we define Randers conformal change as where σ ( x ) is a function of x and β ( x, y ) = b i ( x ) y i is a 1- form on M n . This transformation is more general as it includes conformal, Randers and homothetic transformation as particular cases. In the present paper we have found out the expressions for scalar curvature and main scalar of two-dimensional Finsler space obtained by Randers conformal change of F n . We have also obtained equation of geodesic for this transformed space.