Related papers: Notes on isotropic geometry of production models
Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula…
Toric topology emerged in the end of the 1990s on the borders of equivariant topology, algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly grown up into a very active area with many interdisciplinary…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…
We classify complete orientable hypersurfaces of constant isotropic curvature in space forms. We show that such a hypersurface has constant mean curvature only if it is an isoparametric hypersurface, and that it is minimal if and only if it…
The relationship between micro-structure and macro-structure of complex systems using information geometry has been dealt by several authors. From this perspective, we are going to apply it as a geometrical structure connecting both…
During the past thirty years hyperbolic type metrics have become popular tools also in modern mapping theory, e.g., in the study of quasiconformal and quasiregular maps in the euclidean $n$-space. We study here several metrics that one way…
In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
We make a systematic investigation of quadrature properties for quadrics, namely integration of holomorphic functions over planar domains bounded by second degree curves. A full understanding requires extending traditional settings by…
The existing combinatorial methods for iso-surface computation are efficient for pure visualization purposes, but it is known that the resulting iso-surfaces can have holes, and topological problems like missing or wrong connectivity can…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their `concavity index', $m$. Such polygons are called \emph{$m$-convex} polygons and are characterised by…
We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…