Related papers: Clifford Parallelisms and External Planes to the K…
The presence of compact extra dimensions in cosmological scenarios in the context of f(T)-like gravities is discussed. For the case of toroidal compactifications, the analysis is performed in an arbitrary number of extra dimensions.…
For smooth projective curves the Clifford index is an important invariant which provides a bound for the dimension of the space of sections of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper…
We define a super analog of the classical Pl\"{u}cker embedding of the Grassmannian into a projective space. One of the difficulties of the problem is rooted in the fact that super exterior powers $\Lambda^{r|s}(V)$ are not a simple…
In previous publications I have proposed a geometrical framework underpinning the local, realistic, and deterministic origins of the strong quantum correlations observed in Nature, without resorting to superdeterminism, retrocausality, or…
Let ${\mathcal G}_k(V)$ be the $k$-Grassmannian of a vector space $V$ with $\dim V=n$. Given a hyperplane $H$ of ${\mathcal G}_k(V)$, we define in [I. Cardinali, L. Giuzzi, A. Pasini, A geometric approach to alternating $k$-linear forms, J.…
The exceptional compact hermitian symmetric space EIII is the quotient $E_6/Spin(10)\times_{\mathbb{Z}_4}U(1)$. We introduce the Pl\"ucker coordinates which give an embedding of EIII into $\mathbb{C}P^{26}$ as a projective subvariety. The…
We highlight the relation between the projective geometries of $n$-dimensional Euclidean, spherical and hyperbolic spaces through the projective models of these spaces in the $n+1$-dimensional Minkowski space, using a cross ratio notion…
In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural one-to-one correspondence between Clifford quadratic…
We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a…
We construct Grassmann spaces associated with the incidence geometry of regular and tangential subspaces of a symplectic copolar space, show that the underlying metric projective space can be recovered in terms of the corresponding…
Orthogonal spaces are vector spaces together with a quadratic form whose associated bilinear form is non-degenerate. Over fields of characteristic two, there are many quadratic forms associated to a given bilinear form and quadratic…
For a symplectic vector space $V$, a projective subvariety $Z \subset {\bf P} V$ is a Legendrian variety if its affine cone $\widehat{Z} \subset V$ is Lagrangian. In addition to the classical examples of subadjoint varieties associated to…
We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.
We present pictorial means of distinguishing contravariant vectors (or simply vectors) from covariant vectors (or linear forms). When one depicts vector as the directed segment, then the pictorial image of a linear form is a family of…
The paper is devoted to projective Clifford groups of quantum $N$-dimensional systems. Clearly, Clifford gates allow only the simplest quantum computations which can be simulated on a classical computer (Gottesmann-Knill theorem). However,…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
In this paper we embed $m$-dimensional Euclidean space in the geometric algebra $Cl_m $ to extend the operators of incidence in ${R^m}$ to operators of incidence in the geometric algebra to generalize the notion of separator to a decision…
This note provides an intrinsic construction of the Carrollian superplane $\Pi \mathbb{S}\simeq \mathbb{R}^{2|4}$ as a supermanifold generalisation of the Carrollian plane. Moving away from the $c\rightarrow 0$ limit of relativistic…
Betten and Riesinger constructed Parallelisms of $\mathop{\rm PG}(3,\mathbb R)$ with automorphism group $\mathop{\rm SO}(3,\mathbb R)$ by applying the reducible $\mathop{\rm SO}(3,\mathbb R)$-action to a rotational Betten spread. This was…
We propose two alternative formulations for a three-dimensional non-anticommutative superspace in which some of the fermionic coordinates obey Clifford anticommutation relations. For this superspace, we construct the supersymmetry…