Related papers: Structure D'Un Drapeau Riemannien

We prove that for any element in the $\gamma$-completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its $\gamma$-support is a smooth Lagrangian submanifold, then the element itself is a smooth…

We extend the classification of homogeneous codimension-one foliations on irreducible Riemannian symmetric spaces of noncompact type obtained by Berndt and Tamaru to the reducible case, thus completing it for all noncompact symmetric…

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…

In this paper we study the homology of a random Cech complex generated by a homogeneous Poisson process in a compact Riemannian manifold M. In particular, we focus on the phase transition for "homological connectivity" where the homology of…

This paper provides a characterization of homogeneous curves on a geometric flag manifold which are geodesic with respect to any invariant metric. We call such curves homogeneous equigeodesics. We also characterize homogeneous equigeodesics…

R. Zimmer proved that, on a compact manifold, a foliation with a dense leaf, a suitable leafwise Riemannian symmetric metric and a transverse Lie structure has arithmetic holonomy group. In this work we improve such result for totally…

Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$.…

We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…

If M is a riemannian manifold, then the inclusion of the complex of coclosed harmonic forms into the de Rham complex induces a linear isomorphism in cohomology. If M has at most countably many connected components, this linear isomorphism…

We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…

In this paper we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold we present a construction of a canonical flat F-manifold associated to it. We also describe a…

This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance…

We classify all simply connected Riemannian manifolds whose isotropy groups act with cohomogeneity less than or equal to two.

The question whether a Riemannian manifold is geodesically connected can be studied from geometrical as well as variational methods, and accurate results can be obtained by using the associated distance and related properties of the…

We call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian…

We consider closed manifolds that possess a so called rank one ray structure. That is a (flat) affine structure such that the linear part is given by the products of a diagonal transformation and a commuting rotation. We show that closed…

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by a result of Heintze and Liu, and associate to such a submanifold M and a point x in M a canonical homogeneous…

On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete…

In this paper, we consider a Riemannian foliation whose normal bundle carries a parallel or harmonic basic form. We estimate the norm of the O'Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…