Cartan connection of transversally Finsler foliation
The purpose of this paper is to define transversal Cartan connection of Finsler foliation and to prove its existence and uniqueness.
Cauchy-Riemann submanifolds of Kaehlerian Finsler spaces.
We study the geometry of the second fundamental form of a Cauchy-Riemann submanifold of a Kaehlerian Finsler space M2n; any totally-real submanifold of M2n with v-flat normal connection is shown to be a Berwald-Cartan space.
Characterizations of the nonlinear connection in the higher order geometry.
Classification of Randers metrics of scalar flag curvature.
Complete Finsler manifolds and adapted coordinates.
Complex geodesics and Finsler metrics
Complex Lagrange spaces.
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 Finsler manifolds
Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection (‘pull-back formalism’), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.
Connections in -vector bundles.
Critical point theorems on Finsler manifolds.
Crofton formulas in projective Finsler spaces.
Crofton measures in polytopal Hilbert geometries.
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 .