Duality and minimality in Riemannian foliations.
Duality of Hodge numbers of compact complex nilmanifolds
A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
Duality Principle and Special Osserman Manifolds
Duality Properties of Characteristic Forms.
Dubins' problem is intrinsically three-dimensional
Dubins' problem is intrinsically three-dimensional
In his 1957 paper [1] L. Dubins considered the problem of finding shortest differentiable arcs in the plane with curvature bounded by a constant and prescribed initial and terminal positions and tangents. One can generalize this problem to non-euclidean manifolds as well as to higher dimensions (cf. [15]). Considering that the boundary data - initial and terminal position and tangents - are genuinely three-dimensional, it seems natural to ask if the n-dimensional problem always reduces to the...
D'un résultat hilbertien à un principe de comparaison entre spectres. Applications
Dupin Hypersurfaces.
Dupin'sche Hyperflächen in E4.
Dynamical connections and non-autonomous lagrangian systems
Dynamique des flots unipotents sur les espaces homogènes
-degeneration and -lemma
For a double complex , we show that if it satisfies the -lemma and the spectral sequence induced by does not degenerate at , then it degenerates at . We apply this result to prove the degeneration at of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of -lemma.
Earthquakes are analytic.
Editorial note : “Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres”
Effondrement des variétés riemanniennes
Effondrement, spectre et propriétés diophantiennes des flots riemanniens
On étudie le comportement des premières valeurs propres du laplacien agissant sur les formes différentielles lors d’un effondrement adiabatique d’un flot riemannien sur une variété compacte . Le nombre de petites valeurs propres peut alors se calculer en fonction de la cohomologie basique de , et on donne des critères spectraux pour l’annulation des classes d’Álvarez et d’Euler du flot. En outre, on définit un invariant de nature diophantienne du flot qui est lié au comportement asymptotique...
Efimov's theorem in dimension greater than two.
Eigenfunctions and Nodal Sets
Eigenspaces of Invariant Differential Operators on an Affine Symmetric Space.
Eigenvalue Comparison Theorems and Its Geometric Applications.