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Relation between algebraic and geometric view on NURBS tensor product surfaces

Dalibor Martišek, Jana Procházková (2010)

Applications of Mathematics

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.

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

Archivum Mathematicum

Consider a flat symplectic manifold ( M 2 l , ω ) , l 2 , 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 λ is an eigenvalue of the symplectic Dirac operator such that - ı l λ is not a symplectic Killing number, then l - 1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.

Relative K-stability of extremal metrics

Jacopo Stoppa, Gábor Székelyhidi (2011)

Journal of the European Mathematical Society

We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.

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