The Jacobi fields for a spray on the tangent bundle.
The Jordan normal form of higher order Osserman algebraic curvature tensors
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type in a vector space of signature . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
The kaehlerian structures and reproducing kernels
It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.
The Kähler Ricci flow on Fano manifolds (I)
We study the evolution of pluri-anticanonical line bundles along the Kähler Ricci flow on a Fano manifold . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of . For example, the Kähler Ricci flow on converges when is a Fano surface satisfying or . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....
The Killing Tensors on an -dimensional Manifold with -structure
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
The Kuranishi space of complex parallelisable nilmanifolds
We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic symplectic in even dimension. We describe the Kuranishi space in detail in several examples and also analyse when small deformations remain complex parallelisable.
The metric in gauge theory: an introduction and some applications
We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.
The -dual of an Finsler space of order two.
The -Cohomology of
The L2-Structure of Moduli spaces of Einstein Metrics on 4-Manifolds.
The Lagrange rigid body motion
We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group with its natural...
The Laplace spectrum and Hermitian spaces.
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...
The laplacian and the Dirac operator in infinitely many variables
The laplacian on asymptotically flat manifolds and the specification of scalar curvature
The Lefschetz type theorem for a class of noncompact mappings
The Legendre transformation
The length spectrum of riemannian two-step nilmanifolds
The level crossing problem in semi-classical analysis. II. The Hermitian case
This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.
The Lie derivative and cohomology of -structures.