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In this talk, we are mainly concerned with invariant geometric flows in affine-related geometries including centro-equiane, centro-affine, affine and affine-symplectic geometries. First, we show that ...
The phase function and polarized phase function are important optical parameters, which describe scattering properties of atmospheric aerosol particles. Polarization of skylight induced by the scatter...
A wide range of applications requires an accurate description of the physical phenomena occurring in complex geometrical domains. The exploitation of subsurface resources or the geological disposal of...
We study the local geometry of irreducible parabolic geometries admitting strongly essential ows; these are ows by local automorphisms with higher-order xed points. We prove several new rigidit...
We use the general theory developed in our article [1] in the setting of parabolic geometries to reprove known results on special in nitesimal automorphisms of projective and conformal geometries.
We study vector elds generating a local ow by automorphisms of a parabolic geometry with higher order xed points. We develop general tools extending the techniques of [1], [2], and [3], and we a...
We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that in nitesimal automorphis...
The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, a...
We present a new method for the solution of the Stokes equations. The main features of our method are: (1) it can be applied to arbitrary geometries in a black-box fashion; (2) it is second-order accu...
Abstract: Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital alg...
Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures...
We prove that if a Calabi–Yau manifold M admits a holomorphic Cartan geometry, then M is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on com...
We show that if E ⊂ Fdq , the d-dimensional vector space over the finite field with q elements,and |E| ≥ qd, where q−1 2 ≪  ≤ 1, then E contains an isometric copy of at least cd&#...
R´esum´e. Une analyse des propri´et´es g´eom´etriques d’une structure relatives `a un reduit est entam´ee. En particulier la d´efinissabilit´e des...

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