A dynamical approach to compactify the three dimensional Lorentz group.
A few remarks on the geometry of the space of leaf closures of a Riemannian foliation
The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space. In Section...
A Fiber bundle theorem.
A finiteness theorem for Riemannian submersions
Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.
A finiteness theorem for the space of harmonic sections.
A Foliated Metric Rigidity Theorem for Higher Rank Irreducible Symmetric Spaces.
A Formula for Popp’s Volume in Sub-Riemannian Geometry
For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub- Laplacian, namely the one associated with Popp’s volume. Finally, we discuss...
A framed structure on a -tangent manifold.
A framed -structure on tangent manifolds.
A framed structure on the cotangent bundle of a Hamilton space.
A framed f-structure on the tangent bundle of a Finsler manifold
Let (M,F) be a Finsler manifold, that is, M is a smooth manifold endowed with a Finsler metric F. In this paper, we introduce on the slit tangent bundle a Riemannian metric G̃ which is naturally induced by F, and a family of framed f-structures which are parameterized by a real parameter c≠ 0. We prove that (i) the parameterized framed f-structure reduces to an almost contact structure on IM; (ii) the almost contact structure on IM is a Sasakian structure iff (M,F) is of constant flag curvature...
A Frankel type theorem for CR submanifolds of Sasakian manifolds
We prove a Frankel type theorem for submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about submanifolds of Sasakian space forms.
A fully nonlinear version of the Yamabe problem on manifolds with boundary
We propose to study a fully nonlinear version of the Yamabe problem on manifolds with boundary. The boundary condition for the conformal metric is the mean curvature. We establish some Liouville type theorems and Harnack type inequalities.
A Function Defined on an Even-dimensional Real Submanifold of a Hermitian Manifold
A functorial approach to differential characters.
A gauge theoretical approach to space-time structures
A general comparison theorem with applications to volume estimates for submanifolds
A general non-linear convexity theorem.
A general optimal inequality for arbitrary Riemannian submanifolds.
A General Schwarz Lemma for Riemannian-Manifolds