Submanifolds of an even-dimensional manifold structured by a -parallel connection.
Submanifolds of Constant Mean Curvature.
Submanifolds of Euclidean space with parallel mean curvature vector.
Submanifolds of -structure manifold satisfying .
Submanifolds of -structure manifold satisfying .
Submanifolds with Flat Normal Bundle.
Submanifolds with Geodesic Normal Sections.
Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry
We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.
Submanifolds with harmonic mean curvature vector field in contact 3-manifolds
Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated.
Submanifolds with Prescribed Mean Curvature Vector.
Submersion of CR-submanifolds of locally conformal Kähler manifold.
Subriemannian geodesics of Carnot groups of step 3
In Carnot groups of step ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.
Sub-riemannian metrics : minimality of abnormal geodesics versus subanalyticity
Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...
Sub-riemannian sphere in Martinet flat case
Sub-Riemannian sphere in Martinet flat case
This article deals with the local sub-Riemannian geometry on ℜ3, (D,g) where D is the distribution ker ω, ω being the Martinet one-form : dz - ½y2dxand g is a Riemannian metric on D. We prove that we can take g as a sum of squares adx2 + cd2. Then we analyze the flat case where a = c = 1. We parametrize the set of geodesics using elliptic integrals. This allows to compute the exponential mapping, the wave front, the conjugate and cut loci and the sub-Riemannian sphere. A direct consequence...
Subspaces of recurrent Finsler spaces.
Subtleties concerning conformal tractor bundles
The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor bundles and...
Sufficiency Conditions Under Which a Lagrangian is an Ordinary Divergence.
Sufficient conditions for convexity in manifolds without focal points
In this paper, local, global, strongly local and strongly global supportings of subsets in a complete simply connected smooth Riemannian manifold without focal points are defined. Sufficient conditions for convexity of subsets in the same sort of manifolds have been derived in terms of the above mentioned types of supportings.