Certain types of affine motion in a Finsler manifold. I
Certain types of affine motion in a Finsler manifold. II
Certain types of affine motion in a Finsler manifold. III
Classification of Randers metrics of scalar flag curvature.
Commutation formulas for -differentiation in a generalized Finsler space
Complex sprays and complex curves.
After defining what is meant by a complex spray X on a complex manifold M, we introduce the notion of a spray complex curve associated to X. Several equivalent formulations are derived and we give necessary and sufficient conditions for M to admit spray complex curves for X through each point and in each direction. Refinements of this result are then derived for some special cases, for example when X is the horizontal radial vector field associated to a complex Finsler metric.
Conformal ℱ-harmonic maps for Finsler manifolds
By introducing the ℱ-stress energy tensor of maps from an n-dimensional Finsler manifold to a Finsler manifold and assuming that (n-2)ℱ(t)'- 2tℱ(t)'' ≠ 0 for any t ∈ [0,∞), we prove that any conformal strongly ℱ-harmonic map must be homothetic. This assertion generalizes the results by He and Shen for harmonics map and by Ara for the Riemannian case.
Conformal vector fields on tangent bundle of Finsler manifolds.
Conformally closed Finsler spaces.
Connections in -vector bundles.
Criteria for conformal flatness of Finsler spaces.
Curvature theory of generalized connection in .
Cut and singular loci up to codimension 3
We give a new and detailed description of the structure of cut loci, with direct applications to the singular sets of some Hamilton-Jacobi equations. These sets may be non-triangulable, but a local description at all points except for a set of Hausdorff dimension is well known. We go further in this direction by giving a classification of all points up to a set of Hausdorff dimension .