Related papers: Conformal vector fields on Finsler manifolds

Studying various functionals and associated gradient ows are known problems in differential geometry. The perpose of this article is to provide a general overview of curvature functionals in Finsler geometry and use their information for…

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…

We present for the first time a Friedmann-like construction in the framework of an osculating Finsler-Randers-Sasaki geometry. In particular, we consider a vector field in the metric on a Lorentz tangent bundle, and thus the curvatures of…

We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…

The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields…

We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…

Before retiring, looking back to forty years of writing and publishing scientific papers, I decided to present to the scientific community a selection of my scientific works. I chose mostly articles published in prestigious journals or…

Torse-forming vector fields are generalizations of some important vector fields. In this paper, we present some techniques to transform a proper torse-forming vector field into its special cases. Concrete examples are given.

Based on a self-contained, coordinate-free exposition of the necessary concepts and tools of spray and Finsler geometry (with detailed proofs), we derive new results among others on the consequences of the direction-independence of the…

We construct connection maps and linear symmetric connections on tangent and second-order tangent bundles for \fr manifolds using the notion of a spray. For these manifolds, we characterize linear symmetric connections on tangent bundles in…

In this paper, using the Finslerian settings, we study the existence of parallel one forms (or, equivalently parallel vector fields) on a Riemannian manifold. We show that a parallel one form on a Riemannian manifold M is a holonomy…

We study conformal tractor bundles from an extrinsic viewpoint, relating them to codimension two spacelike immersions into Lorentzian manifolds. We show that, at least locally, every Riemannian conformal structure admits a natural…

I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a…

We provide unipotent factorizations of vector bundle automorphisms of real and complex vector bundles over smooth manifolds. This generalises work of Thurston-Wasserstein and Wasserstein for trivial vector bundles. We also address two…

In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…

In this paper, we define almost paracontact and normal almost paracontact Finsler structures on a vector bundle and find some conditions for integrability of these structures. We define paracontact metric, para- Sasakian and K-paracontact…

Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violating. The directional dependence of the Finsler metric provides a way to encode the Lorentz violating effects into the geometric structure…

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities…

We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…

We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping…