Weyl-ambient geometries

Weyl Structures for Parabolic Geometries

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces G/P with G semisimple and P parabolic, Weyl structures and preferred connections are introduced in this general framework. In particular, we extend the notions of scales, closed and exact Weyl connections, and Rho–tensors, we characterize the classes of such...

Higher Order Gravity , Gauge Invariant Variables , And Quantum Behavior In Weyl - Like Geometries

This paper presents the detailed, standard treatment of a simple, gauge invariant action for Weyl and Weyl-like Cartan geometries outlined in a previous paper. In addition to the familiar scalar curvature squared and Maxwell terms, the action chosen contains the logarithmic derivative of the scalar curvature combined with the intrinsic four vector (Weyl vector) in a gauge invariant fashion. Thi...

Generalized Douglas-Weyl Finsler Metrics

In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

A Necessary Condition for Weyl-Heisenberg Frames

On Special Generalized Douglas-Weyl Metrics

In this paper, we study a special class of generalized Douglas-Weyl metrics whose Douglas curvature is constant along any Finslerian geodesic. We prove that for every Landsberg metric in this class of Finsler metrics, ? = 0 if and only if H = 0. Then we show that every Finsler metric of non-zero isotropic flag curvature in this class of metrics is a Riemannian if and only if ? = 0.