Related papers: A Diagram for Bianchi A-Types
We construct open descendants of Gepner models, concentrating mainly on the six-dimensional case, where they give type I vacua with rich patterns of Chan-Paton symmetry breaking and various numbers of tensor multiplets, including zero. We…
We study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in…
All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates.…
Conformal block divisors in type A on $\bar{M}_{0,{n}}$ are shown to satisfy new symmetries when levels and ranks are interchanged in non-standard ways. A connection with the quantum cohomology of Grassmannians reveals that these divisors…
A plane symmetric Bianchi-I model is explored in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of energy-momentum tensor. The solutions are obtained with the consideration of a specific Hubble parameter which yields a…
We consider flows of Spin(7)-structures. We use local coordinates to describe the torsion tensor of a Spin(7)-structure and derive the evolution equations for a general flow of a Spin(7)-structure on an 8-manifold M. Specifically, we…
We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show the soliton is rigid in dimensions three and four. In the steady case, we give a complete…
The 1+3 covariant equations, embedded in an extended tetrad formalism and describing a space-time with an arbitrary energy-momentum distribution, are reconsidered. It is shown that, provided the 1+3 splitting is performed with respect to a…
In this work, we will explore the effects of non-commutativity in fractional classical and quantum schemes using the anisotropicc Bianchi Type I cosmological model coupled to a scalar field in the K-essence formalism. We introduce…
Explicit formulas for the $G_2$-components of the Riemannian curvature tensor on a manifold with a $G_2$ structure are given in terms of Ricci contractions. We define a conformally invariant Ricci-type tensor that determines the…
Here is an example of a plane set of vanishing area and consisting of line-segments whose directions cover an angle : let E be a Cantor set of dissection ratio 1/4 (therefore dimension 1/2) carried by the horizontal axis and E' the image of…
Suppose $\Cal R$ is the complement of an essential arrangement of toric hyperlanes in the complex torus $(\C^*)^n$ and $\pi=\pi_1(\Cal R)$. We show that $H^*(\Cal R;A)$ vanishes except in the top degree $n$ when $A$ is one of the following…
A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmological string is investigated. The objective of this study is to generate solutions to the Einstein equations using a few tractable assumptions usually…
We present the exact equation for evolution of Bianchi I cosmological model, considering a non-tilted perfect fluid in a matter dominated universe. We use the definition of shear tensor and later we prove it is consistent with the evolution…
In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here…
Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann-Robertson-Walker background model. This connects the…
We investigate the triviality of compact Ricci solitons under general scalar conditions involving the Weyl tensor. More precisely, we show that a compact Ricci soliton is Einstein if a generic linear combination of divergences of the Weyl…
We prove in a simple and coordinate-free way the equivalence bteween the classical definitions of the mass or the center of mass of an asymptotically flat manifold and their alternative definitions depending on the Ricci tensor and…
A self-consistent system of interacting spinor and scalar fields is considered within the scope of Bianchi type VI cosmological model filled with a perfect fluid. The contribution of the cosmological constant ($\Lambda$-term) is taken into…
In this paper we report on a local classification of four dimensional Ricci solitons which have a $2$-dimensional Abelian Killing algebra $\mathcal{G}_{2}$, whose Killing leaves are non-null and orthogonally intransitive. The classification…