相关论文: The geometry of product conjugate connections

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the…

The paper observes an almost Hermitian manifold as an example of a generalized Riemannian manifold and examines the application of a quarter-symmetric connection on the almost Hermitian manifold. The almost Hermitian manifold with…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

In this paper, almost product-like Riemannian manifolds are investigated. Basic properties on tangential hypersurfaces of almost product-like Riemannian manifolds are obtained. Some examples of tangential hypersurfaces are presented. Some…

A classical tensor product $A \,\otimes\, B$ of complete lattices $A$ and $B$, consisting of all down-sets in $A \times B$ that are join-closed in either coordinate, is isomorphic to the complete lattice $Gal(A,B)$ of Galois maps from $A$…

We study the semistability of the tensor product of hermitian vector bundles by using the $\varepsilon$-tensor product and the geometric (semi)stability of vector subspaces in the tensor product of two vector spaces.

In this paper we address what generalized geometric structures are possible on products of spaces that each admit generalized geometries. In particular we consider, first, the product of two odd dimensional spaces that each admit a…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

The characteristic connection of an almost hermitian structure is a hermitian connection with totally skew-symmetric torsion. The case of parallel torsion in dimension six is of particular interest. In this work, we give a full…

Symmetric products of curves are important spaces for both geometers and topologists, and increasingly useful objects for physicists. We summarize in this note some of their basic homotopy theoretic properties and derive a handful of known…

Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a…

On Hermitian manifolds, the second Ricci curvature tensors of various metric connections are closely related to the geometry of Hermitian manifolds. By refining the Bochner formulas for any Hermitian complex vector bundle (Riemannain real…

Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for…

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…