Biharmonic maps between doubly warped product manifolds.
Biharmonic Riemannian maps
We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo-umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the target manifolds.
Biharmonic submanifolds in 3-dimensional -manifolds.
Biholomorphic curvature of an almost Hermitian manifold.
Bi-Legendrian connections
We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on .
Bilinear forms and extremal Kähler vector fields associated with Kähler classes.
Bilinéarité et géométrie affine attachées aux espaces de spineurs complexes, minkowskiens ou autres
BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that BZcan be decomposed into a controlled number of pieces, the restriction of f on each of which is quantitatively biLipschitz. This extends a result of [14], which proved the same result, but with the restriction that G has an appropriate discretization. We provide an example of a Carnot group not admitting such...
Bilipschitz invariance of the first transverse characteristic map
Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class C¹ by H. Natsume.
Biminimal Legendrian surfaces in 5-dimensional Sasakian space forms
We classify nonminimal biminimal Legendrian surfaces in 5-dimensional Sasakian space forms.
Biminimal submanifolds in contact 3-manifolds.
Biot-Savart-Laplace dynamical systems.
Birational equivalence in the symplectic category.
Biwave maps into manifolds.
Blow-up of regular submanifolds in Heisenberg groups and applications
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence...
Bochner and Schoenberg theorems on symmetric spaces in the complex case
Bochner flat Kahlerian manifolds.
Bochner's formula for harmonic maps from Finsler manifolds
Let ϕ :(M,F)→ (N,h) be a harmonic map from a Finsler manifold to any Riemannian manifold. We establish Bochner's formula for the energy density of ϕ and maximum principle on Finsler manifolds, from which we deduce some properties of harmonic maps ϕ.
Bochner's theorem and minimal foliation. (Théorème de Bochner et feuilletage minimal.)
Bohm Aharonov effects for bounded states in the case of systems