On affine transformations of Banachable bundles
On Berwald and Wagner manifolds.
On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach
In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.
On -planar mappings of affine-connection spaces with infinite dimension
On hypersurfaces in a locally affine Riemannian Banach manifold. II.
On hypersurfaces in a locally affine Riemannian Banach manifold.
On the geometry of some para-hypercomplex Lie groups
In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in...
On the geometry of the Virasoro-Bott group.
On the Kähler geometry of the Hilbert-Schmidt Grassmannian.
On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds
The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.
On the radical of J*-triples.
On the Structure of Manifolds with positive Scalar Curvature.
Operator inequalities, geodesics and interpolation
Plateau-Stein manifolds
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
Plongements lipschitziens dans un espace pentagonal
Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.
The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal...
Projective bundles on infinite-dimensional complex spaces.
Remarks on the cohomological classification of certain Fréchet bundles.
Riemannian geometries on spaces of plane curves
We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms of , acting as reparametrizations. In particular we investigate the metric, for a constant , where is the curvature of the curve and , are normal vector fields to . The term is a sort of geometric Tikhonov regularization because, for , the geodesic distance between any two distinct curves is 0, while for the...
Riemannian structures and -homology. (Structures riemanniennes et -homologie.)