See also
 | This article about a French mathematician is a stub. You can help Wikipedia by expanding it. |
Arthur Besse is a pseudonym chosen by a group of French differential geometers, led by Marcel Berger, following the model of Nicolas Bourbaki. A number of monographs have appeared under the name.
| This article about a French mathematician is a stub. You can help Wikipedia by expanding it. |
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.
In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition is equivalent to saying that the metric is a solution of the vacuum Einstein field equations, although both the dimension and the signature of the metric can be arbitrary, thus not being restricted to the four-dimensional Lorentzian manifolds usually studied in general relativity. Einstein manifolds in four Euclidean dimensions are studied as gravitational instantons.
In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. For flat connections, the associated holonomy is a type of monodromy and is an inherently global notion. For curved connections, holonomy has nontrivial local and global features.
Mikhael Leonidovich Gromov is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of IHÉS in France and a Professor of Mathematics at New York University.
Jean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups, and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields.
In differential geometry, a quaternion-Kähler manifold is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some . Here Sp(n) is the sub-group of consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic matrix, while the group of unit-length quaternions instead acts on quaternionic -space by right scalar multiplication. The Lie group generated by combining these actions is then abstractly isomorphic to .
The Séminaire Nicolas Bourbaki is a series of seminars that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of mathematical achievement, fashion, and reputation. It is named after Nicolas Bourbaki, a group of French and other mathematicians of variable membership.
In Riemannian geometry, a branch of mathematics, harmonic coordinates are a certain kind of coordinate chart on a smooth manifold, determined by a Riemannian metric on the manifold. They are useful in many problems of geometric analysis due to their regularity properties.
In mathematics, L2 cohomology is a cohomology theory for smooth non-compact manifolds M with Riemannian metric. It is defined in the same way as de Rham cohomology except that one uses square-integrable differential forms. The notion of square-integrability makes sense because the metric on M gives rise to a norm on differential forms and a volume form.
In differential geometry, a quaternion-Kähler symmetric space or Wolf space is a quaternion-Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion-Kähler symmetric space with positive Ricci curvature is compact and simply connected, and is a Riemannian product of quaternion-Kähler symmetric spaces associated to compact simple Lie groups.
Marcel Berger was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Formerly residing in Le Castera in Lasseube, Berger was instrumental in Mikhail Gromov's accepting positions both at the University of Paris and at the IHÉS.
In mathematics — specifically, in differential topology — Berger's inequality for Einstein manifolds is the statement that any 4-dimensional Einstein manifold (M, g) has non-negative Euler characteristic χ(M) ≥ 0. The inequality is named after the French mathematician Marcel Berger.
In Riemannian geometry, a branch of mathematics, the prescribed Ricci curvature problem is as follows: given a smooth manifold M and a symmetric 2-tensor h, construct a metric on M whose Ricci curvature tensor equals h.
Mikhail Mikhailovich Postnikov was a Soviet mathematician, known for his work in algebraic and differential topology.
In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic flow on the tangent space of the manifold.
In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29, 1976 in a letter to David Kazhdan as an analogue of the usual Fourier transform. It was used by Gérard Laumon to simplify Deligne's proof of the Weil conjectures.
Wilhelm Paul Albert Klingenberg was a German mathematician who worked on differential geometry and in particular on closed geodesics.
In mathematics, a Novikov–Shubin invariant, introduced by Sergei Novikov and Mikhail Shubin (1986), is an invariant of a compact Riemannian manifold related to the spectrum of the Laplace operator acting on square-integrable differential forms on its universal cover.
Sylvestre F. L. Gallot is a French mathematician, specializing in differential geometry. He is an emeritus professor at the Institut Fourier of the Université Grenoble Alpes, in the Geometry and Topology section.
Paul Gauduchon is a French mathematician, known for his work in the field of differential geometry. He is particularly known for his introduction of Gauduchon metrics in hermitian geometry. His textbook on spectral geometry, written with Marcel Berger and Edmond Mazet, is a standard reference in the field.