We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This unifies the complete lift defined by I.Satô and the horizontal lift introduced by S.Ishihara and K.Yano. We study some geometric properties of this lift and its compatibility with symplectic forms on the cotangent bundle.

In this article we give a classi cation of the binary, simple, ω−categorical structures with SU−rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of nite structures equipped with a probability measure. This study give results about general almost sur...

Let An denote the number of objects of some type of “size” n, and let Cn denote the number of these objects which are connected. It is often the case that there is a relation between a generating function of the Cn’s and a generating function of the An’s. Wright showed that if limn→∞Cn/An = 1, then the radius of convergence of these generating functions must be zero. In this paper we prove that...

In this paper, we prove necessary and sufficient conditions for a smooth surface in a smooth 4-manifold X to be pseudoholomorphic with respect to an almost complex structure on X. In particular, this provides a systematic approach to the construction of pseudoholomorphic curves that do not minimize the genus in their homology class.

in this paper,  we introduce  the notion of $m$-fuzzifying interval spaces, and discuss the relationship between $m$-fuzzifying interval spaces and $m$-fuzzifying convex structures.it is proved that  the category  {bf mycsa2}  can be embedded in  the category  {bf  myis}  as a reflective subcategory, where  {bf mycsa2} and   {bf  myis} denote  the category of $m$-fuzzifying convex structures of...