On Codimension-one Foliations of Constant Mean Curvature.
On foliations of ... By minimal hypersurfaces.
On foliations of differential spaces
On foliations with leaves satisfying some geometrical conditions [Book]
On -G-foliations
On Lie algebras of vector fields related to Riemannian foliations
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
On localization in holomorphic equivariant cohomology
We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.
On riemannian foliations with minimal leaves
For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is , a simple characterization of this geometrical property is proved.
On Riemannian tangent bundles.
On some directions in the development of jet calculus
Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliated manifold morphisms are presented. Although the paper has mainly a survey character, it also includes new results: jets modulo multifoliations are introduced and their relation to (R,S,Q)-jets is demonstrated.
On the first secondary invariant of Molino's central sheaf
For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.
On the group of real analytic diffeomorphisms
The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.
On the integrability of orthogonal distributions in Poisson manifolds.
On the jets of foliation respecting maps
Using Weil algebra techniques, we determine all finite dimensional homomorphic images of germs of foliation respecting maps.
On the linearization theorem for proper Lie groupoids
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...
On the real secondary classes of transversely holomorphic foliations
In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space of the real secondary classes to the space of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also...
On the role of partial Ricci curvature in the geometry of submanifolds and foliations
Submanifolds and foliations with restrictions on q-Ricci curvature are studied. In §1 we estimate the distance between two compact submanifolds in a space of positive q-Ricci curvature, and give applications to special classes of submanifolds and foliations: k-saddle, totally geodesic, with nonpositive extrinsic q-Ricci curvature. In §2 we generalize a lemma by T. Otsuki on asymptotic vectors of a bilinear form and then estimate from below the radius of an immersed submanifold in a simply connected...
On the spectrum of Riemannian submersions with totally geodesic fibers
In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.
On the topological invariance of the basic cohomology.
On transverse structures of foliations