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The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative multiplications invariant with respect to the symmetric bilinear form determined…
Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified…
This note studies Arveson's curvature invariant for d-contractions specialized to the case d=1 of a single contraction operator on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a…
The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature…
We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are…
Warped product manifolds with p-dimensional base, p=1,2, satisfy some curvature conditions of pseudosymmetry type. These conditions are formed from the metric tensor g, the Riemann-Christoffel curvature tensor R, the Ricci tensor S and the…
We study the existence of a non-spacelike isometry, \zeta, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…
A quantum sl(2,R) coalgebra is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the non-constant curvature analogues of the spherical, hyperbolic and (anti-)de Sitter spaces.…
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
It is shown that the variational derivative of the integral of Branson's Q-curvature is the ambient obstruction tensor of Fefferman-Graham. A classification of irreducible conformally invariant tensors modulo quadratic and higher degree…
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…
Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions…
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 argue that the curvature generated by a gravitational field can be used to calculate the corresponding metric which determines the trajectories of freely falling test particles. To this end, we present a method to compute the metric from…
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [arXiv:0812.4776]. We find the algebraic construction to be related to a particular…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature…
It is developed the considerations from (S. M. Min\v{c}i\'c, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for…