Related papers: Geodesics on path spaces and double category

We study non-positively curved closed manifolds $M$ and $n$-dimensional totally geodesic submanifolds of $M \times M$ which satisfy a transversality condition. We prove that, under some mild irreducibility requirements on $M$, if $M \times…

We introduce a new class of zero-dimensional weighted complete intersections, by abstracting the essential features of rational cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a…

We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces $M=G/K$ whose isotropy representation decomposes into a direct sum of three submodules…

The question whether a Riemannian manifold is geodesically connected can be studied from geometrical as well as variational methods, and accurate results can be obtained by using the associated distance and related properties of the…

Let M be a Margulis spacetime whose associated complete hyperbolic surface S has compact convex core. Generalizing the correspondence between closed geodesics on M and closed geodesics on S, we establish an orbit equivalence between…

The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…

We show geodesic completeness of certain compact locally symmetric pseudo-Riemannian manifolds of signature $(2,n)$. Our model space $\mathbf{X}$ is a $1$-connected, indecomposable symmetric space of signature $(2,n)$, that admits a unique…

Let $M_k$ be the complete, simply connected, Riemannian 2-manifold of constant curvature $k \le 0$. Let $E$ be a closed, simply connected subspace of $M_k$ with the property that every two points in $E$ is connected by a rectifiable path in…

The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define the geometric mean of probability measures…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmueller space for any choice of pseudo-Anosov mapping class. As a consequence one obtains a classification of the elements of…

We investigate homogeneous geodesics in a class of homogeneous spaces called $M$-spaces, which are defined as follows. Let $G/K$ be a generalized flag manifold with $K=C(S)=S\times K_1$, where $S$ is a torus in a compact simple Lie group…

We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on…

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…

We formulate geodesics on a manifold in terms of a parallel transfer of a particle state vector transformed by local Lorentz and Yang-Mills symmetry groups. This formulation leads to an introduction of a canonical one-form the eigenvalues…

In this article we derive a complete classification of all submanifolds in space forms with codimension two for which the Gauss map is homothetic.

Let $M=G/H$ be a compact, simply connected, Riemannian homogeneous space, where $G$ is (almost) effective and $H$ is a simple Lie group. In this paper, we first classify all $G$-naturally reductive metrics on $M$, and then all $G$-geodesic…

We study the existence of closed geodesics on compact Riemannian orbifolds, and on noncompact Riemannian manifolds in the presence of a cocompact, isometric group action. We show that every noncontractible Riemannian manifold which admits…

Let $V$ be a separable Hilbert space, possibly infinite dimensional. Let $\St(p,V)$ be the Stiefel manifold of orthonormal frames of $p$ vectors in $V$, and let $\Gr(p,V)$ be the Grassmann manifold of $p$ dimensional subspaces of $V$. We…

A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic characterization of geodesic orbit manifolds that are…