Related papers: Spacelike Foliations on Lorentz manifolds
The space ML(F) of measured geodesic laminations on a given closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (earthquake theory) or complex projective (grafting)…
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…
The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave…
In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space $\mathbb{S}_1^{m+1}(c)$, under some geometric constraints. Our results extend the understanding…
New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is…
In this paper, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in spatially open Robertson-Walker spacetimes whose fiber is flat. Moreover, our results…
The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.
On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geometry of such a surface is codified by this function. The…
In this paper we consider some properties of the three-dimensional homogeneous SO(2)-isotropic Riemannian manifolds. In particular, we determine the geodesics, the totally geodesic surfaces, the totally umbilical surfaces and the geodesics…
We consider closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordstr\"{o}m manifolds. By using a new integral formula or Brendle's Heintze-Karcher…
Let $\mathcal{F}$ be a codimension one holomorphic foliation in $\mathbb{P}^n$, $n\geq 2$, leaving invariant a real-analytic Levi-flat hypersurface $M$ with regular part $M^{*}$. Then every leaf of $\mathcal{F}$ outside $\overline{M^{*}}$…
This note provides an alternative proof of a result of Labourie. We show that the two complements of the convex core of a three dimensional quasi-fuchsian hyperbolic manifold may be foliated by embedded hypersurfaces of constant Gaussian…
Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau…
We prove a result which establishes restrictions on the pseudoholomorphic curves which can exist in a stable Hamiltonian manifold in the presence of certain $\mathbb{R}$-invariant foliations of the symplectization by holomorphic…
In this work we perform a general study of properties of a class of locally symmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetime decomposition. The hypersurfaces are given by specifying the form of the Ricci tensor…
Let $f:M\to M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded…
A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the condition that the second fundamental form is proportional to the metric. It is also a generalization of the notion of a…
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
In this Note we establish a relation between sections in globally generated holomorphic vector bundles on K\"ahler manifolds, isotropic with respect to a non-degenerate quadratic form, and totally geodesic foliations on Euclidean open…
We show that many Lorentzian manifolds of dimension >2 do not admit a spacelike codimension-one foliation, and that almost every manifold of dimension >2 which admits a Lorentzian metric at all admits one which satisfies the dominant energy…