This paper provides a new perspective to the problem of reconfiguration of a rolling sphere. It is shown that the motion of a rolling sphere can be characterized by evoluteinvolute geometry. This characterization, which is a manifestation of our specific selection of Euler angle coordinates and choice of angular velocities in a rotating coordinate frame, allows us to recast the three-dimensiona...

Classical (real) hedgehogs can be regarded as the geometrical realiza-tions of formal di¤erences convex bodies in R n+1. Like bodies, identi…ed with their support functions. Adopting a pro-jective viewpoint, we prove that any holomorphic function h : C n ! 'support function' complex hedgehog H In same vein, introduce notion evolute such 2 , and natural (but apparently hitherto unknown) curvatur...

We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.

Various services supports are the principal requirements of the Fourth Generation (4G) system; therefore, the need to improve integration of heterogeneous networks is significant. This paper amends EVOLUTE (a project of Information Society Technologies (IST)) to strengthen mobility management. This paper uses Multicast-based Mobility (M&M) to aid Cellular IP (CIP) in micro-mobility management. ...

The quaternionic KP hierarchy is the integrable hierarchy of p.d.e obtained by replacing the complex numbers with the quaternions in the standard construction of the KP hierarchy and its solutions; it is equivalent to what is often called the Davey-Stewartson II hierarchy. This article studies its relationship with the theory of conformally immersed tori in the 4-sphere via quaternionic holomor...

A Riemannian manifold satis es the axiom of 2-planes if at each point, there are su ciently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several de nitions of axiom of planes arise naturally when we consider such families of tangent planes...

In this paper, we classify evolute offsets of a ruled surface in Minkowski 3-space L with constant Gaussian curvature and mean curvature. As a result, we investigate linear Weingarten evolute offsets of a ruled surface in L .

Let XR be a geometrically irreducible smooth projective curve, defined over R, such that XR does not have any real points. Let X = XR×R C be the complex curve. We show that there is a universal real algebraic line bundle over XR × Pic d(XR) if and only if χ(L) is odd for L ∈ Picd(XR). There is a universal quaternionic algebraic line bundle over X × Pic(X) if and only if the degree d is odd. Tak...

We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces Af with quaternionic multiplication attached to a normalized newform f without complex multiplication. We include an example of Af with quaternionic multiplication for which we find numerically a curve C whose Jacobian is Af up to numerical approximation, and we prove that it...