Abstract Using harmonic mean curvature flow, we establish a sharp Minkowski-type lower bound for total of convex surfaces with given area in Cartan-Hadamard $3$-manifolds. This inequality also improves the known estimates hyperbolic $3$-space. As an application, obtain Bonnesen-style isoperimetric distance function nonpositively curved $3$-spaces, via monotonicity results curvature. connection ...

The goal of this paper is to express the Bach tensor of a four dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach te...

Starting from a real analytic surface ℳ with conformal Cartan connection A. Bor´owka constructed minitwistor space of an asymptotically hyperbolic Einstein–Weyl manifold being the boundary. In this article, starting symmetry connection, we prove that symmetries on can be extended to obtained manifold.

A contact path geometry is a family of paths in a contact manifold each of which is everywhere tangent to the contact distribution and such that given a point and a one-dimensional subspace of the contact distribution at that point there is a unique path of the family passing through the given point and tangent to the given subspace. A contact projective structure is a contact path geometry the...

A contact path geometry is a family of paths in a contact manifold each of which is everywhere tangent to the contact distribution and such that given a point and a one-dimensional subspace of the contact distribution at that point there is a unique path of the family passing through the given point and tangent to the given subspace. A contact projective structure is a contact path geometry the...

Theory of General Relativity is considered from the point of view of its general structure; it has been showed that if one assumes any connection to be a metric connection then Cartan tensor must necessary be completely antisymmetric, and an example of application is considered in the case of Lie group theory. Under a geometrical point of view, Cartan tensor is thought to represent the Torsion ...

A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein–Cartan theory and the possible interpretation of the torsion trace as the electromagnetic potential. Starting with a Lagrangian built of Dirac spinors, orthonormal tetrads, and a complex rather than a real linear connection we define an...

The book “Handbook of Finsler geometry” has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein’s vacuum field equations was treated. In this example, the calculation of the components of the hv-curvature of Cartan connection leads to wrong expressions. On the o...