Related papers: Geometric classification of real ternary octahedra…
Employing ideas of noncommutative geometry, certain dimensional invariant for quantum homogeneous spaces has been proposed and here we take up its computation for quaternion spheres.
We study tetrahedral quartics in projective space. We address their projective geometry, Neron-Severi lattice and automorphism group.
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
Classifications and representations are two main topics in the theory of quadratic forms. In this paper, we consider these topics of ternary quadratic forms. For a given squarefree integer $N$, first we give the classification of positive…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
We describe all possible arrangements of the ten nodes of a generic real determinantal quartic surface in $\Cp3$ with nonempty spectrahedral region.
K3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the standard tetrahedron. Exploring these combinatorial objects, we…
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schr\"odinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that…
We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…
Chiral tetrahedral molecules can be dealt under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules. It is shown that a quaternionic representation…
In this work we give the classification of real ternary cubic forms with respect to rank and border rank up to SL(3)-action and we examine the differences with the complex case.
We identify the algebra of regular functions on the space of quartic polynomials in three complex variables invariant under SL(3,C) with an algebra of meromorphic automorphic forms on the complex 6-ball. We also discuss the underlying…
We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group: isoparametric surfaces, surfaces with constant principal curvatures, homogeneous surfaces, and…
We classify quadratic spaces over endomorphism fields of K3 surfaces. We consider both totally real and CM cases.
We describe special Ka\"hler geometry, special quaternionic manifolds, and very special real manifolds and analyze the structure of their isometries. The classification of the homogeneous manifolds of these types is presented.
A positive-definite integral quadratic form is called regular if it represents every positive integer which is locally represented. In this article, we classify all regular diagonal quadratic forms of rank greater than 3.