Related papers: Geodesics on adjoint orbits of $SL(n, \mathbb{R})$

Deciding whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. This paper takes a step towards understanding a broad class of nonconvex-nonconcave minimax problems that do remain…

In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…

We explore the existence of closed geodesics and geodesic spirals for the Szeg\"o metric in a $C^{\infty}$-smoothly bounded strongly pseudoconvex domain $\Omega\subset\mathbb{C}^n$, which is not simply connected for $n \geq 2$.

For any maximal surface group representation into $\mathrm{SO}_0(2,n+1)$, we introduce a non-degenerate scalar product on the the first cohomology group of the surface with values in the associated flat bundle. In particular, it gives rise…

The method of constructing spectral Darboux coordinates on finite dimensional coadjoint orbits in duals of loop algebras is applied to the one pole case, where the orbit is identified with a coadjoint orbit in the dual of a finite…

We study the geodesics problem in Heisenberg group H (case SR and riemannian). The sheaf of infinitesimal automorphisms of the (2n,2n+1) distribution D over H is an infinite, transitive Lie algebra sheaf.

We show that any second order dynamic equation on a configuration space $X\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\to X$ of relativistic…

We found some Lagrangian submanifolds of the adjoint semisimple orbit in two cases. For the first, the compact case, also known as the Generalized flag manifolds, we prove that the real flags can be seen as infinitesimally tight Lagrangian…

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…

In this paper, we obtain an infinite dimensional Lie algebra of exotic gauge invariant observables that is closed under Goldman-type bracket associated with monodromy matrices of flat connections on a compact Riemann surface for $G_{2}$…

The so-called Sasaki projection was introduced by U. Sasaki on the lattice L(H) of closed linear subspaces of a Hilbert space H as a projection of L(H) onto a certain sublattice of L(H). Since L(H) is an orthomodular lattice, the Sasaki…

The aim of this paper is the study of the geodesic distance in operator groups with several Riemannian metrics. More precisely we study the geodesic distance in self-adjoint operator groups with the left invariant Riemannian metric induced…

In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every…

We consider $H$(eisenberg)-type groups whose law of left translation gives rise to a bracket generating distribution of step 2. In the contrast with sub-Riemannian studies we furnish the horizontal distribution with a nondegenerate…

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with…

We quantise orbits of the adjoint group action on elements of the sl(2,R) Lie algebra. The path integration along elliptic slices is akin to the coadjoint orbit quantization of compact Lie groups, and the calculation of the characters of…

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

In recent work, we related the structure of subvarieties of $n\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\mathbb{C})$-orbits on the flag variety of $\mathfrak{gl}(n,\mathbb{C})$. In the first part of this…

In this paper we prove geometric residue theorems for bundle maps over a compact manifold. The theory developed associates residues to the singularity submanifolds of the map for any invariant polynomial. The theory is then applied to a…

This is the content of a talk given by the author at the 2009 Lehigh University Geometry/Topology Conference. Using the definition of connection given by Dieudonn\'e, the Sasaki metric on the tangent bundle to a Riemannian manifold is…