The spread of the shape operator as conformal invariant.
The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics
In this paper we investigate analytic affine control systems q̇ = X + uY, u ∈ [a,b] , where X,Y is an orthonormal frame for a generalized Martinet sub-Lorentzian structure of order k of Hamiltonian type. We construct normal forms for such systems and, among other things, we study the connection between the presence of the singular trajectory starting at q0 on the boundary of the reachable set from q0 with the minimal number of analytic functions needed for describing the reachable set from q0.
The symmetric tensor Lichnerowicz algebra and a novel associative Fourier-Jacobi algebra.
The Tanaka-Webster connection for almost -manifolds and Cartan geometry
We prove that a CR-integrable almost -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal...
The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time.
The volume of geodesic disks in a Riemannian manifold
The volumes of small geodesic balls for a metric connection
The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles
Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers, Élie Cartan...
Theorems concerning certain special tensor fields on Riemannian manifolds and their applications.
Theory of semisymmetric conformally flat and biharmonic submanifolds.
Theory of the zero order effect suitable to investigate the space-time geometrical properties.
TheStructure of Nearly Kähler Manifolds.
Three dimensional near-horizon metrics that are Einstein-Weyl
We investigate which three dimensional near-horizon metrics admit a compatible 1-form such that defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.
Timelike -slant helices in Minkowski space
We consider a unit speed timelike curve in Minkowski 4-space and denote the Frenet frame of by . We say that is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction of . In this work we study those helices where the function is constant and we give different characterizations of such curves.
Timelike quaternion frame of a non-lightlike curve.
Torsion and the second fundamental form for distributions
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry.
Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds
Total absolute curvature of curves in Lorentz Manifolds
Totally real submanifolds of a complex space form.
Totally real surfaces in with parallel mean curvature vector.