Related papers: Geodesic orbit spaces in real flag manifolds
A Lie group G has many left invariant metrics having drastically different curvature properties. If we regard G as a flat and globalizable absolute parallelism as in [O1], then G has a canonical metric. We study some surprising consequences…
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…
This short note has been written as an Oberwolfach report for the workshop "Differentialgeometrie im Grossen". We discuss properties of metric spaces that at almost all points admit a tangent metric space. We explain why, under some mild…
We characterize strongly Morse quasi-geodesics in Outer space as quasi-geodesics which project to quasi-geodesics in the free factor graph. We define convex cocompact subgroups of $Out(F_n)$ as subgroups such that an orbit map in the free…
Einstein's equations of gravitation are not invariant under geodesic mappings, i. e. under a certain class of mappings of the Christoffel symbols and the metric tensor which leave the geodesic equations in a given coordinate system…
Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical…
We study homogeneous curves on some classes of reductive homogeneous spaces G=H which are geodesics with respect to any G-invariant metric on G=H. These curves are called equigeodesics. The spaces we consider are certain Stiefel manifolds…
Orbits of test particles and light rays are an important tool to study the properties of space-time metrics. Here we systematically study the properties of the gravitational field of a globally regular magnetic monopole in terms of the…
It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to a algebraic system, if $g$ is a $G$-invariant metric. In this paper we described this system for all flag manifolds of a classical Lie group. We…
The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…
We use the Hopf fibration to explicitly compute generators of the second homotopy group of the flag manifolds of a compact Lie group. We show that these $2$-spheres have nice geometrical properties such as being totally geodesic surfaces…
We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the…
A smooth curve on a homogeneous manifold $G/H$ is called a Riemannian equigeo-desic if it is a homogeneous geodesic for any $G$-invariant Riemannian metric. The homogeneous manifold $G/H$ is called Riemannian equigeodesic, if for any $x\in…
In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces then we give the flag curvature formula of them. Also we study the special cases of…
A naturally parameterised curve in a Lie group with a left invariant metric is a geodesic, if its tangent vector left-translated to the identity satisfies the Euler equation $\dot{Y}=\operatorname{ad}^t_YY$ on the Lie algebra $\mathfrak{g}$…
A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of…
A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in…
In this note we give an example of a one-dimensional manifold with two connected components and a complete metric whose group of isometries has an orbit which is not closed. This answers a question of S. Gao and A. S. Kechris.
We deal with compact Kaehler manifolds M which are acted on by a semisimple compact Lie group G of isometries with codimension one regular orbits. We provide an explicit description of the standard blow-ups of such manifolds along complex…
We consider the complex ind-group $G=\mathrm{SL}(\infty,\mathbb{C})$ and its real forms $G^0=\mathrm{SU}(\infty,\infty)$, $\mathrm{SU}(p,\infty)$, $\mathrm{SL}(\infty,\mathbb{R})$, $\mathrm{SL}(\infty,\mathbb{H})$. Our main objects of study…