In this paper, we define a new projective invariant and call it W̃ -curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃ -curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.

The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in [8] for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold M , that depends on a pseudo-Riem...

Surface splatting has developed into a valuable alternative to triangle meshes when it comes to rendering of highly detailed massive datasets. However, even highly accurate splat approximations of the given geometry may sometimes not provide a sufficient rendering quality since surface lighting mostly depends on normal vectors whose deviation is not bounded by the Hausdorff approximation error....

The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen and S. Gutt showed that the action of the group of Hamiltonian diffeomorphisms on this space is Hamiltonian and calculated the moment map. This is analogous to, but distinct from, the action of Hamiltonian diffeomorphisms on the space of compatible almost complex structures that motivates study o...

We show that an abelian surface embedded in P by a very ample line bundle L of type (1, 2d) is projectively normal if and only if d ≥ 4. This completes the study of the projective normality of abelian surfaces embedded by complete linear systems. Mathematics Subject Classifications (2000): Primary, 14K05; secondary, 14N05, 14E20.

The ideals generated by pfaffians of mixed size contained in a subladder of a skew-symmetric matrix of indeterminates define arithmetically Cohen-Macaulay, projectively normal, reduced and irreducible projective varieties. We show that these varieties belong to the G-biliaison class of a complete intersection. In particular, they are glicci.

We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked out, one of them yielding a quantum length element on S3.

On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density S of fixed weight λ. In particular, this implies that on any projectively connected manifold, a ‘bracket’ (symmetric biderivation) on the algebra of functions extends canonically to the algebra of densities.

This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are inadequate. In the course of this examination, this thesis builds theoretical foundations for IEEE 754 floating-point numbers, interval arithmetic based on the project...