Related papers: On closed geodesics in Lorentz manifolds
In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the…
Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses in finite…
We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface…
We introduce a new technique to the study and identification of submanifolds of simply-connected symmetric spaces of compact type based upon an approach computing $k$-positive Ricci curvature of the ambient manifolds and using this…
We solve explicitly the geodesic equation for a wide class of (pseudo)-Riemannian homogeneous manifolds (G/H,m), including those with G compact, as well as non-compact semisimple Lie groups, under a simple algebraic condition for the metric…
We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.
This is a survey paper. We explain the known constructions for two geometrically different classes of examples of compact Riemannian 7-manifolds with holonomy G2. One method uses resolutions of singularities of appropriately chosen…
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…
Brinkmann Lorentz manifolds are those admitting an isotropic parallel vector field. We prove geodesic completeness of the compact and also compactly homogeneous Brinkmann spaces. We also prove, partially, that their parallel vector field…
On each compact, connected, orientable surface of genus greater than one we construct a class of flows without self-similarities.
This paper is a review of recent results on integrable nonholonomic geodesic flows of left--invariant metrics and left- and right--invariant constraint distributions on compact Lie groups.
We give existence results for simple closed curves with prescribed geodesic curvature on $S^{2}$, which correspond to periodic orbits of a charge in a magnetic field.
In this paper we describe the topological behavior of the geodesic flow for a class of closed 3-manifolds realized as quotients of nonstrictly convex Hilbert geometries, constructed and described explicitly by Benoist. These manifolds are…
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine…
Let (X,\omega) be a compact K\"ahler manifold. As discovered in the late 1980s by Mabuchi, the set H_0 of K\"ahler forms cohomologous to \omega has the natural structure of an infinite dimensional Riemannian manifold. We address the…
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any sets with asymptotic density with respect to a specific norm. We…
We make some remarks on the existence of a geodesically complete core for any compact non-positively curved space.
Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric…