Related papers: L2-transverse conformal Killing forms on complete …

We prove that the L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L^2 metric is a weak Riemannian metric, this fact does not…

For a normal covering over a closed oriented topological manifold we give a proof of the L2-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove…

An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the…

We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed with a conformal Killing vector field.

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality…

If the Killing vector field in a Riemannian manifold is the gradient of a smooth real valued function, then it is called Killing potential. In this paper we have deduced a necessary condition for the existence of Killing potential in a…

We develop the theory of twisted L^2-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on the first de Rham cohomology of M and they generalize the standard…

We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not…

We construct a natural conformally invariant one-form of weight $-2k$ on any $2k$-dimensional pseudo-Riemannian manifold which is closely related to the Pfaffian of the Weyl tensor. On oriented manifolds, we also construct natural…

In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness…

In the present paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We…

This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic…

It is well known that, by the Reeb stability theorem, the leaf space of a Riemannian foliation with compact leaves is an orbifold. We prove that, under mild completeness conditions, the leaf space of a Killing Riemannian foliation is a…

In this article, we study the geometric properties of codimension one foliations on Riemannian manifolds equipped with vector fields that are closed and conformal. Apart from its singularities, these vector fields define codimension one…

We study left-invariant foliations $\mathcal{F}$ on Riemannian Lie groups $G$ generated by a subgroup $K$. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations…

This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics…

We study N=2 superconformal theories on Euclidean and Lorentzian four-manifolds with a view toward applications to holography and localization. The conditions for supersymmetry are equivalent to a set of differential constraints including a…

We prove that any dual leaf $L^{\#}$ of a simply connected, complete nonnegatively curved polar manifold $M$ is totally geodesic and closed in $M$, and $L^{\#}$ is itself a complete nonnegatively curved polar manifold. Furthermore, the dual…

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about…

In Kaehler manifolds are investigated conformally flat totally real submanifolds, which are semiparallel or have semiparallel mean curvature vector.