-valued differential forms on
1 Structure de contact et équations aux dérivées partielles d'après V. V. Lychagin
A Hodge type decomposition for spinor valued forms
A Reduction Theorem for Cohomology Groups of Very Strongly q-convex Kähler Manifolds.
An Elementary Proof for a Compact Imbedding Result in Generalized Electromagnetic Theory.
Anti-self-dual orbifolds with cyclic quotient singularities
An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...
Canonical equivariant extensions using classical Hodge theory.
Combinatorial Hodge Theory and Signature Operator.
Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity
For odd-dimensional Poincaré–Einstein manifolds , we study the set of harmonic -forms (for ) which are (with ) on the conformal compactification of . This set is infinite-dimensional for small but it becomes finite-dimensional if is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology and the kernel of the Branson–Gover [3] differential operators on the conformal infinity . We also relate the set of forms in the kernel of to the conformal...
Courants positifs extrêmaux et conjecture de Hodge.
De Rham-Hodge Theory for Riemannian Foliations.
Décomposition de Hodge basique pour un feuilletage riemannien
Soit un feuilletage de codimension sur une variété compacte . On montre que le complexe des formes basiques admet une décomposition de Hodge. Il en résulte que la cohomologie basique de est de dimension finie et vérifie la dualité de Poincaré si et seulemnt si .
Déviations de moyennes ergodiques, flots de Teichmüller et cocycle de Kontsevich-Zorich
Étant donnée une fonction régulière de moyenne nulle sur le tore de dimension , il est facile de voir que ses intégrales ergodiques au-dessus d’un flot de translation “générique”sont bornées. Il y a une dizaine d’années, A. Zorich a observé numériquement une croissance en puissance du temps de ces intégrales ergodiques au-dessus de flots d’hamiltoniens (non-exacts) “génériques”sur des surfaces de genre supérieur ou égal à , et Kontsevich et Zorich ont proposé une explication (conjecturelle) de...
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.
Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups
We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then for some unitary representation . By our earlier work there exists a -closed holomorphic 1-form with coefficients twisted by some unitary representation , possibly non-isomorphic to . Taking norms we obtains a positive...
Formes harmoniques et cohomologie relative des algèbres de Lie.
Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
Harmonic cohomology classes of symplectic manifolds.
Harmonic mappings of Kähler manifolds to locally symmetric spaces
Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).