Regularization of currents and entropy
NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.
Consider a flat symplectic manifold , , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If is an eigenvalue of the symplectic Dirac operator such that is not a symplectic Killing number, then is an eigenvalue of the symplectic Rarita-Schwinger operator.
All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).
We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.