Let f : X −→ S be a smooth projective family and let (L, h) be a singular hermitian line bundle on X with semipositive curvature current. Let Ks := K(Xs, KXs +L | Xs, h | Xs)(s ∈ S) be the Bergman kernel of KXs +L | Xs with respect to h | Xs and let hB the singular hermitian metric on KX + L defined by hB |Xs := 1/Ks. We prove that hB has semipositive curvature. This is a generalization of the ...

Motor planning is the process of preparing the appropriate motor commands in order to achieve a goal. This process has largely been thought to occur before movement onset and traditionally has been associated with reaction time. However, in a virtual line bisection task we observed an overlap between movement planning and execution. In this task performed with a robotic manipulandum, we observe...

This paper presents an automated classification system of landform elements based on object-oriented image analysis. First, several data layers are produced from Digital Terrain Models (DTM): elevation, profile curvature, plan curvature and slope gradient. Second, relatively homogenous objects are delineated at several levels through image segmentation. These object primatives are classified as...

we prove that every r-quadratic metric of scalar flag curvature with a dimension greater than twois of constant flag curvature. then we show that generalized douglas-weyl metrics contain r-quadraticmetrics as a special case, but the class of r-quadratic metric is not closed under projective transformations

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

One of the basic problems of Riemannian geometry is the classification of manifolds of positive sectional curvature. The known examples include the spherical space forms which carry constant curvature metrics and the rank 1 symmetric spaces whose canonical metrics have sectional curvatures at each point varying between 1 and 4. In 1951 H.E. Rauch [18] introduced the notion of curvature pinching...

Let M be a compact k-dimensional riemmanian manifold minimally immersed in the unit n-dimensional sphere S. It is easy to show that for any p ∈ S the boundary of the geodesic ball in S with radius π2 and center at p (in this case this boundary is an equator) must intercept the manifold M . When the codimension is 1, i.e. k = n − 1, it is known that the ricci curvature, is not greater than 1. We...