Proper homothetic vector fields in Bianchi type-I space-time.
We consider almost-complex structures on whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an “exotic” integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary condition for the nondegeneration of the Frölicher spectral sequence at the second level.
This paper studies the smoothness and the curvature of conflict sets of the distance function in the plane. Conflict sets are also well known as 'bisectors'. We prove smoothness in the case of two convex sets and give a formula for the curvature. We generalize moreover to weighted distance functions, the so-called Johnson-Mehl model.
If is a convex surface in a Euclidean space, then the squared intrinsic distance function is DC (d.c., delta-convex) on in the only natural extrinsic sense. An analogous result holds for the squared distance function from a closed set . Applications concerning -boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface are given.
It is shown that operators occurring in the classical Penrose transform are differential. These operators are identified depending on line bundles over the twistor space.
A product preserving functor is a covariant functor from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: . It is known that any product preserving functor is equivalent to a Weil functor . Here is the set of equivalence classes of smooth maps and are equivalent if and only if for every smooth function the formal Taylor series at 0 of and are equal in . In this paper all...
The paper is devoted to Euclidean space motions with two straight trajectories on two given skew straight lines. It describes all motions from this class which have one more planar trajectory in a plane not parallel to the given lines. In the conclusion it given conditions under which such motions have further planar trajectories in planes not parallel to the given skew straight lines.
Dans cet article, nous étudions le flot des chambres de Weyl d’une large classe de sous-groupe discrets d’un groupe de Lie semi-simple réel : les groupes de Ping-Pong. Nous montrons que ce flot est mélangeant relativement à la mesure de Patterson-Sullivan ; celle-ci étant infinie en rang , nous précisons cette propriété de mélange en explicitant sa vitesse dans le direction du vecteur de croissance du groupe.
We study global properties of the twistor space over an even dimensional conformally flat manifold, proving that the twistor space is Kähler if and only if the manifold is conformally equivalent to the standard -dimensional sphere ().
On donne une description algébrique de l’ensemble des classes d’isomorphisme d’espaces symétriques affines connexes, simplement connexes et projectivement plats. On en déduit une classification des espaces symétriques affines connexes et projectivement plats et on détermine tous les espaces symétriques affines connexes admettant une transformation projective non affine.