The nonexistence of rank 4 IP tensors in signature .
The osculating hyperquadrics of the three-component distribution in affine space
The Plane-Time in Which Paths of Inertional Motions Are Conics
The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions
Our aim is to study the principal bundles determined by the algebra of quaternions in the projective model. The projectivization of the conformal model of the Hopf fibration is considered as example.
The reconstruction theorem
The Riemann tensor for nonholonomic manifolds.
The Riemannian curvature tensor and differentiable spaces
The rigidity theorem for Landsberg hypersurfaces of a Minkowski space
Let Mⁿ be a compact Landsberg hypersurface of a Minkowski space with constant mean curvature H. Using the Gauss formula for the Chern connection of Finsler submanifolds, we prove that if M is convex, then M is Riemannian with constant curvature.
The -curvature of homogeneous -metrics.
The Segre imbedding and its converse
The semiring of immersions of manifolds.
The spectral geometry of the Weyl conformal tensor
We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.
The spray and antispray theory in the subspaces of Miron's .
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