Differential Geometry of Spray and Finsler Spaces

By Zhongmin Shen. 2001

609 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9fa90b3ae4da13d6f74fac369372ca6a7194c7ea

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In Astronomy and Astrophysics

Citations in the corpus

Randers metrics with special curvature properties (2003, methodology): “According to [8], the S-curvature of = α + β is given by”
On generalized Douglas–Weyl (α, β)-metrics (2015, background): “For example, Shen proved that the Bishop-Gromov volume comparison holds for Finsler manifolds with vanishing S-curvature [14].”
On the definition and examples of Finsler metrics (2011, background): “(1) Our definition of (standard) Finsler metric agrees with classical references as [1, 2, 5, 12, 34, 44, 45] and our definition of conic Finsler metric is equivalent to the notion of generalized Finsler metric by [10] (but we retain our nomenclature as we are also dealing with other generalizations”
Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties (2008, background): “In Finsler geometry, there are several geometric quantities: the Riemann curvature (the flag curvature), the distortion, the (mean) Cartan curvature, the S-curvature, the (mean) Landsberg curvature and the (mean) Berwald curvature, etc. (Cf. [7] [8]).”
RANDERS METRICS OF SCALAR FLAG CURVATURE (2009, background): “([ 13 ]) F is of scalar flag curvature K = K(x,y) if and only if in a standard local coordinate system,”
A class of Finsler metrics with isotropic S-curvature (2009, background): “An important property is that S = 0 for Berwald spaces with respect to the Busemann-Hausdorff volume form dVBH [10][11].”
Differential Geometry of Special Mappings (2019, background): “Riemann-Finsler space is a Berwald space if Gijk = 0, and a Riemann-Finsler space is a weakly Berwald space if Gijα = Gij = 0, see [161].”