Hermitian natural tensors.
Une homotopie régulière , , dans une variété symplectique est dite inactive si en chaque point le déplacement infinitésimal est -orthogonal à l’espace tangent de l’objet déplacé. Si est un polyèdre de de dimension et si est un ouvert de , toute homotopie de jusqu’à est déformable en une homotopie régulière inactive. On donne une application à l’engouffrement en géométrie symplectique.
Regarding the generalized Tanaka-Webster connection, we considered a new notion of -parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂm+2) and proved that a real hypersurface in G 2(ℂm+2) with generalized Tanaka-Webster -parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP n in G 2(ℂm+2), where m = 2n.
We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in and prove non-existence of real hypersurfaces in with generalized Tanaka-Webster...
We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of -holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.