Géométrie différentielle affine des hypersurfaces
Geometry and analytic theory of Frobenius manifolds.
Geometry of Cyclic and Anticylic Algebras
The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function.
Geometry of holomorphic distributions of real hypersurfaces in a complex projective space
We characterize homogeneous real hypersurfaces ’s of type , and of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution of .
Geometry of k-Lagrange Spaces of Second Order
Geometry of parallelizable manifolds in the context of generalized Lagrange spaces.
“Geometry” of spin 3 gauge theories
Geometry of the rolling ellipsoid
We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....
Geometry of third order ODE systems
We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application.
Global Gronwall estimates for integral curves on Riemannian manifolds.
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.
Grassmannian structures on manifolds.
Harmonic 4-Spaces.
Harmonic curvatures in Lorentzian space.
Harmonic morphisms between degenerate semi-Riemannian manifolds.
Harmonic morphisms between semi-Riemannian manifolds.
Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures
2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.
Higher covariant derivatives.
Higher order Codazzi tensors on conformally flat spaces.
Higher order connections.
Higher order contact of real curves in a real hyperquadric