Related papers: Sub-twistor metrics

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple…

We briefly review the hierarchy for the hyper-K\"ahler equations and define a notion of symmetry for solutions of this hierarchy. A four-dimensional hyper-K\"ahler metric admits a hidden symmetry if it embeds into a hierarchy with a…

In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic…

In this paper, we answer some natural questions on symmetrisation and more general combinations of Finsler metrics, with a view towards applications to Funk and Hilbert geometries and to metrics on Teichm{\"u}ller spaces. For a general…

For a standard Finsler metric F on a manifold M, its domain is the whole tangent bundle TM and its fundamental tensor g is positive-definite. However, in many cases (for example, the well-known Kropina and Matsumoto metrics), these two…

The sub-Finslerian geometry means that the metric $F$ is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Rinow theorem is proved in the case of sub-Finslerian…

We define the notion of sub-Finsler geometry as a natural generalization of sub-Riemannian geometry with applications to optimal control theory. We compute a complete set of local invariants, geodesic equations, and the Jacobi operator for…

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions…

The aim of the present paper is to provide a global presentation of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and most commonly…

We consider the group of sense-preserving diffeomorphisms $\Diff S^1$ of the unit circle and its central extension, the Virasoro-Bott group, with their respective horizontal distributions chosen to be Ehresmann connections with respect to a…

Twistor CR manifolds, introduced by LeBrun, are Lorentzian (neutral) CR 5-manifolds defined as $\mathbb{P}^1$-bundles over 3-dimensional conformal manifolds. In this paper, we embed a real analytic twistor CR manifold into the twistor space…

We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric…

Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general…

The norm of Cartan torsion plays an important role for studying of immersion theory in Finsler geometry. Indeed, Finsler manifold with unbounded Cartan torsion can not be isometrically imbedded into any Minkowski space. In this paper, we…

We investigate here all the possible invariant metric functions under the action of various kinds of semi-direct product Poincar\'e subgroups and their deformed partners. The investigation exhausts the possible theoretical frameworks for…

We use twistor methods to promote Namikawa's universal Poisson deformations of conic affine symplectic singularities to families of hyperk\"ahler structures deforming hyperk\"ahler cone metrics. The metrics we produce are generally…

We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…

The paper contributes to the important and urgent problem to extend the physical theory of space-time in a Finsler-type way under the assumption that the isotropy of space is violated by a single geometrically distinguished spatial…

In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions.…

Using twistor methods we derive a generating function which leads to the hyperk\" ahler metric on a deformation of the Atiyah-Hitchin monopole moduli space. This deformation was first considered by Dancer through the quotient construction…