Related papers: Classification of invariant AHS--structures on sem…

We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…

In a previous paper, we obtained a cohomological obstruction to the existence of compact manifolds locally modelled on a homogeneous space. In this paper, we give a classification of the semisimple symmetric spaces to which this obstruction…

For an element a in a semigroup S the local subsemigroup of S with respect to a is the subsemigroup aSa of S and the variant of S with respect to a is a semigroup with underlying set S with a sandwich operation xy = xay for all x, y in S.…

In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a…

We obtain a necessary and sufficient condition for the existence of equivariant real structures on complex symmetric spaces for semisimple groups and discuss how to determine the number of equivalence classes for such structures.

In this paper we consider germs of smooth Levi flat hypersurfaces, under the following notion of local equivalence: S_1 ~ S_2 if their one-sided neighborhoods admit a biholomorphism smooth up to the boundary. We introduce a simple invariant…

We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case.

In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.

For a closed locally symmetric space M=\Gamma\G/K and a representation of G we consider the push-forward of the fundamental class in the homology of the linear group and a related invariant in algebraic K-theory. We discuss the…

In this article, we construct in a purely local way partial (Hasse) invariants for $p$-divisible groups with given endomorphisms, using crystalline cohomology. Theses invariants generalises the classical Hasse invariant, and allow us to…

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries.…

We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or…

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.

We classify invariant almost complex structures on homogeneous manifolds of dimension 6 with semi-simple isotropy. Those with non-degenerate Nijenhuis tensor have the automorphism group of dimension either 14 or 9. An invariant almost…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is…

A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of admissible states). In this paper we give local…

We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze…

Having developed a description of indefinite extrinsic symmetric spaces by corresponding infinitesimal objects in the preceding paper we now study the classification problem for these algebraic objects. In most cases the transvection group…

We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or…