Invariant submanifolds of Sasakian manifolds.
Invariant vector fields of Hamiltonians
A complete classification of natural transformations of Hamiltonians into vector fields on symplectic manifolds is given herein.
Invariants homotopiques attachés aux fibrés symplectiques
On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne -orientée dans : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré -symplectique, c’est-à-dire dont le groupe structural est le revêtement à feuillets de . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...
Invariants in contact topology.
Invariants of complex structures on nilmanifolds
Let be a simply connected -dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on compatible with to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving...
Isotopy of sympletic balls, Gromov' s radius and the structure of ruled symplectic 4-manifolds.
Isotropic almost complex structures and harmonic unit vector fields
Isotropic almost complex structures define a class of Riemannian metrics on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.
Isotropic almost complex structures on tangent bundles.
Isotropic characteristic classes
Isotropic sections and curvature properties of hyperbolic Kaehlerian manifolds.