Related papers: Causal simplicity and (maximal) null pseudoconvexi…

We define in the space of n by m matrices of rank n, n less or equal than m, the condition Riemannian structure as follows: For a given matrix A the tangent space of A is equipped with the Hermitian inner product obtained by multiplying the…

Nonrelativistic equation of particle with a spin for the Lagrangian on a nonassociative algebra is obtained. It is shown that in this model arises Riemann-Cartan space. In the case of central symmetry in addition to the pseudo-curvature…

Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci…

We obtain sharp inequalities involving the Ricci curvature and the scalar curvature for anti-invariant Riemannian submersions from Sasakian space forms onto Riemannian manifolds.

We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher-dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null…

We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a…

We introduce a notion of quasiconvexity for continuous functions $f$ defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold $(M,g)$ and $\mathbb{R}^m$, naturally generalizing the classical…

We consider the usual causal structure $(I^+,J^+)$ on a spacetime, and a number of alternatives based on Minguzzi's $D^+$ and Sorkin and Woolgar's $K^+$, in the case where the spacetime metric is continuous, but not necessarily smooth. We…

In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and…

We study tautness properties of a Riemannian foliation by investigating a symmetric 2-tensor associated with the mean curvature of the foliation. As a consequence, we prove a tautness condition for Riemannian foliations on compact manifolds…

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds…

We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two…

We consider a Hamiltonian torus action on a compact connected symplectic manifold M. For a certain class of Lagrangian submanifolds Q of M we show that the image of Q under the momentum map is convex. As an application we complete the…

It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any compact constant mean curvature hypersurface can be covered…

We construct the first known examples of compact pseudo-Riemannian manifolds having an essential group of conformal transformations, and which are not conformally flat. Our examples cover all types $(p,q)$, with $2 \leq p \leq q$.

In this paper we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes and produce an example to verify the existence of such a spacetime. Then we demonstrate that a conformally flat generalized Ricci-recurrent…

We prove a limit curve theorem for incomplete metric spaces. Our main application is to Sormani and Vegas' null distance, where our results give strong control on the Lorentzian lengths of limit curves. We also show that regular…

We prove that any metric measure spacetime arising from a smooth manifold $M$ endowed with a continuous Lorentzian metric $g$ is infinitesimally Minkowskian, under the assumption that $(M, g)$ is causally simple.

For collapsing sequences of Riemannian manifolds which satisfy a uniform lower Ricci curvature bound it is shown that there is a sequence of scales such that for a set of good base points of large measure the pointed rescaled manifolds…

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices,…