Related papers: The Global Embedding Problem of Semi-Riemannian in…

In this paper we consider determining a minimal surface embedded in a Riemannian manifold $\Sigma\times \mathbb{R}$. We show that if $\Sigma$ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated…

The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.

The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of the rotation…

In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…

We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where…

The holonomy algebras of Einstein not Ricci-flat pseudo-Riemannian manifolds of arbitrary signature are classified. As illustrating examples, the cases of Lorentzian manifolds, pseudo-Riemannian manifolds of signature $(2,n)$ and the…

We obtain a dynamical--topological obstruction for the existence of isometric embedding of a Riemannian manifold-with-boundary $(M,g)$: if the first real homology of $M$ is nontrivial, if the centre of the fundamental group is trivial, and…

We study trapped surfaces from the point of view of local isometric embedding into three-dimensional Riemannian manifolds. When a two-surface is embedded into three-dimensional Euclidean space, the problem of finding all surfaces applicable…

For a compact connected Lie group $G$ acting as isometries on a compact orientable Riemannian manifold $M^{n+1},$ and cohomogeneity not equal to 0 or 2, we prove the existence of a nontrivial embedded $G$-invariant minimal hypersurface,…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

In the theory of minimal submanifold, the following problem is fundamental: when does a given Riemannian manifold admit (or does not admit) a minimal isometric immersion into an Euclidean space form of arbitrary dimension? A partial…

We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free…

We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence…

We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…

It is shown that any open Riemann surface can be immersed in any Stein manifold with (volume) density property and of dimension at least 2, if the manifold possesses an exhaustion with holomorphically convex compacts such that their…

In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…

We prove that for any compact manifold of dimension greater than $1$, the set of pseudo-Riemannian metrics having a trivial isometry group contains an open and dense subset of the space of metrics.

Let $G/H$ be a compact homogeneous space, and let $\hat{g}_0$ and $\hat{g}_1$ be $G$-invariant Riemannian metrics on $G/H$. We consider the problem of finding a $G$-invariant Einstein metric $g$ on the manifold $G/H\times [0,1]$ subject to…

The purpose of the present expository paper is to give an account of the recent progress and present status of the classification of solvable Lie groups admitting an Einstein left invariant Riemannian metric, the only known examples so far…

We propose a new strong Riemannian metric on the manifold of (parametrized) embedded curves of regularity $H^s$, $s\in(3/2,2)$. We highlight its close relationship to the (generalized) tangent-point energies and employ it to show that this…