Related papers: Non-Projected Supermanifolds and Embeddings in Sup…
We start a systematic study of non-projected supermanifolds, concentrating on supermanifolds with fermionic dimension 2 and with the reduced manifold a complex projective space. We show that all the non-projected supermanifolds of dimension…
The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in…
We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate…
The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the…
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommutative super surfaces are introduced and it is shown that the…
This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of…
Associated to any supermanifold is a filtration by spaces, referred to as thickenings. It is the objective of this article to study them up to a certain equivalence and then up to isomorphism in the complex-analytic setting. We study them…
A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution,…
We prove that for genus greater than or equal to 5, the moduli space of super Riemann surfaces is not projected (and in particular is not split): it cannot be holomorphically projected to its underlying reduced manifold. Physically, this…
Any algebra herein is intended over a field of characteristic 0. Let $E$ denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional {$\mathbb{Z}_2$-graded-central-simple} $A$ and a supertrace algebra $B$,…
On the Grassmann manifold G (m, n) of m-dimensional subspaces of an n-dimensional projective space P^n, a certain supplementary construction called the normalization is considered. By means of this normalization, one can construct the…
We introduce the equation of n-dimensional totally geodesic submanifolds of a manifold E as a submanifold of the second order jet space of n-dimensional submanifolds of E. Next we study the geometry of n-Grassmannian equivalent connections,…
We consider the Grassman manifold $G(E)$ as the subset of all orthogonal projections of a given Euclidean space $E$ and obtain some explicit formulas concerning the differential geometry of $G(E)$ as a submanifold of $L(E,E)$ endowed with…
We introduce the self-projecting Grassmannian, an irreducible subvariety of the Grassmannian parametrizing linear subspaces that satisfy a generalized self-duality condition. We study its relation to classical moduli spaces, such as the…
A new generalization of Grassmannians in supergeometry, called $\nu-$Grassmannians, are constructed by gluing $\nu-$domains. By a $\nu-$domain, we mean a superdomain with an odd involution say $\nu$ on its structure sheaf, as morphism of…
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.
An embedding of a point-line geometry \Gamma is usually defined as an injective mapping \epsilon from the point-set of \Gamma to the set of points of a projective space such that \epsilon(l) is a projective line for every line l of \Gamma,…
We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in the classical case, they are the projections of the integral…