On complete surfaces with Gaussian curvature zero in 3-sphere
On complex Cartan spaces.
On -complex Finsler spaces.
On complex structures in 8-dimensional vector bundles.
On complexity and motion planning for co-rank one sub-riemannian metrics
In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic case, we study some non-generic generalizations in the analytic case.
On complexity and motion planning for co-rank one sub-Riemannian metrics
In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [CITE]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C∞ case, we study some non-generic generalizations in the analytic case.
On Conditions for Unrectifiability of a Metric Space
We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.
On conditions under which local isometries are motions
On -conformal changes of Riemann-Finsler metrics
On conformal collineations
On Conformal Minimal Immersions of S2 into CPn.
On conformal powers of the Dirac operator on spin manifolds
The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the Dirac operator....
On conformally 2-recurrent spaces
On conformally birecurrent Ricci-recurrent manifolds
On conformally flat hypersurfaces and Guichard's nets.
On Conformally flat hypersurfaces, Curved flats and cyclic systems.
On conformally flat Lorentz parabolic manifolds
We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.
On conformally flat pseudosymmetric spaces.
On conformally recurrent Ricci-recurrent manifolds
On conformally related conformally recurrent metrics. I. Some general results