Related papers: Collapsing regular Riemannian foliations with flat…

In this paper, the existence and uniqueness of foliations by constant mean curvature spheres on asymptotically flat manifolds of nonzero ADM mass in all dimensions were established. (A similar result in the case of positive mass was…

Singular Riemannian Foliations are particular types of foliations on Riemannian manifolds, in which leaves locally stay at a constant distance from each other. Singular Riemannian Foliations in round spheres play a special role, since they…

We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold is Hamiltonian. In this case, we may…

A smooth foliation of a Riemannian manifold is metric when its leaves are locally equidistant and is homogenous when its leaves are locally orbits of a Lie group acting by isometries. Homogenous foliations are metric foliations, but metric…

A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is…

In this article, we deduce a series of integral formulas for a foliated sub-Riemannian manifold, which is a new geometric concept denoting a Riemannian manifold equipped with a distribution ${\mathcal D}$ and a foliation ${\mathcal F}$,…

We prove the nonexistence of a proper singular Riemannian foliation admitting section in compact manifolds of nonpositive curvature. Then we give a global description of proper singular Riemannian foliations admitting sections on Hadamard…

For a proper action by a locally compact group $G$ on a manifold $M$ with a $G$-equivariant Spin-structure, we obtain obstructions to the existence of complete $G$-invariant Riemannian metrics with uniformly positive scalar curvature. We…

Let $M$ be a closed orientable irreducible $3$-manifold such that $\pi_1(M)$ is left orderable. (a) Let $M_0 = M - Int(B^{3})$, where $B^{3}$ is a compact $3$-ball in $M$. We have a process to produce a co-orientable Reebless foliation…

In this work we show that there is a Riemannian groupoid whose orbits are the closures of the leaves of a regular Riemannian foliation on a compact manifold. This groupoid is equivalent (in a generalized sense of Haefliger) with a…

In this paper, we investigate the mean curvature flows for an equifocal submanifold in a symmetric space of compact type and its focal submanifolds as initial data. It is known that equifocal submanifolds of codimension greater than one in…

We describe a local model for any Singular Riemannian Foliation in a neighbourhood of a closed saturated submanifold of a regular stratum. Moreover we construct a Lie groupoid which controls the transverse geometry of the linear…

Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such…

We prove a formula involving the scalar curvature of a Riemannian manifold endowed with a distribution in terms of an adapted orthonormal frame for its tangent bundle. Using the formula, we then investigate the effect of collapsing the…

An orbit-like foliation is a singular foliation on a complete Riemannian manifold $M$ whose leaves are locally equidistant (i.e., a singular Riemannian foliation) and (transversely) infinitesimally homogenous. This class of singular…

We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the…

A foliation of a manifold M is called R-covered if its lift to the universal cover of M has space of leaves R. We show that there are many graph manifolds which admit taut foliations, but which do not admit any R-covered foliations. On the…

A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold with positive sectional curvature has positive Euler characteristic. We prove this conjecture under the additional assumption that the isometry group has…

It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincar\'e Duality) and the tautness of the foliation are closely related. If…

We characterize compact eight-manifolds M which arise as internal spaces in N=1 flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part of the supersymmetry generator is everywhere…