Introduces a new relation between BF theory and gravity.
problem Formulating gauge theories based on 2-connections.
method Categorical generalization of BF theory coupled to gravity.
result Alternative relation between BFCG and gravity.
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48 results for “unimodular gravity”
Unified formalism for Palatini and unimodular gravity using frame bundle canonical forms.
problem Unified formalism for Palatini and unimodular gravity.
method Employing a relationship between Griffiths variational problem and Lepage-equivalent problem, using canonical forms on the first jet of frame bundle.
result Unified formalism for Palatini and unimodular gravity formulated in a geometrical fashion.
The paper defines unimodularity for coisotropic Poisson spaces and discusses invariant volume forms.
problem Understanding unimodularity and invariant volume forms for Hamiltonian dynamics on coisotropic Poisson spaces.
method Introducing multiplicative unimodularity and discussing its properties for coisotropic Poisson homogeneous spaces.
result Existence of invariant volume forms for explicit Hamiltonian systems on coisotropic Poisson spaces.
The paper classifies Sasaki and Vaisman manifolds of unimodular Lie groups.
problem Understanding the structure of Sasaki and Vaisman manifolds on unimodular Lie groups.
method Basic structure theorem and complete classification for simply connected manifolds.
result A complete classification of simply connected Sasaki and Vaisman unimodular Lie groups.
Prove an isoperimetric inequality for compact bodies in 3D contact non-unimodular Lie groups.
problem Isoperimetric inequality for compact bodies in contact non-unimodular 3D Lie groups.
method Prove an isoperimetric inequality.
result Prove an isoperimetric inequality.
Study of unimodular Sasaki and Vaisman Lie groups, determining all modifications explicitly.
problem Classifying unimodular Sasaki and Vaisman Lie groups.
method Applying the technique of modification to determine all homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups explicitly.
result Complete classification of unimodular Sasaki and Vaisman Lie groups.
We study unimodular measures on the space of all pointed Riemannian -manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups of Lie groups. Unimodularity is preserved under weak* limits, and under certain…
Unimodularity criteria for Poisson structures on foliated manifolds are established.
problem Understanding unimodularity in Poisson structures on foliated manifolds.
method Explicit formula for bigraded decomposition of modular vector fields and analysis of the Reeb class.
result Unimodularity of transverse Poisson structure is a necessary condition for semilocal unimodularity.
Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension threemath.DG
Study left invariant Lorentzian metrics on 3D non-unimodular Lie groups.
problem Classify and analyze left invariant Lorentzian metrics on 3D non-unimodular Lie groups.
method Classify metrics up to automorphism, study curvature functions.
result Obtain Ricci operator, scalar curvature, and sectional curvatures as functions of metrics.
This work explores maximal symmetry in unimodular solvmanifolds.
problem Finding metrics with maximal symmetry in unimodular solvmanifolds.
method Analyzing unimodular solvable Lie groups and proving the existence of metrics with maximal symmetry.
result There is always a metric with maximal symmetry in unimodular solvmanifolds.
Non-unimodular foliations have specific geometric properties.
problem Characterizing foliations with non-unimodular properties.
method Computing base-like cohomology to determine tautness.
result Non-unimodular foliations imply specific geometric structures.
Classification of almost contact metric structures on three-dimensional non-unimodular Lie groupsmath.DG
The paper classifies structures on specific Lie groups.
problem Classifying almost contact metric structures on Lie groups.
method Investigation of left-invariant structures on three-dimensional non-unimodular Lie groups.
result Classification of left-invariant almost contact metric structures.
The paper explores the connection between Poisson-Lie structures and invariant volume forms in Hamiltonian dynamics.
problem Understanding the relationship between Poisson-Lie structures and invariant volume forms in Hamiltonian systems.
method Analyzing the existence and preservation of invariant volume forms under Hamiltonian vector fields on Poisson-Lie groups.
result A unimodular Poisson-Lie structure ensures the preservation of a multiple of any left-invariant volume, and the existence of a preserving volume form implies unimodularity.
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.
Paper generalizes results from nilpotent Lie algebras to broader types.
problem Generalizing results from nilpotent Lie algebras to broader types.
method Examined Einstein Lorentzian unimodular and solvable Lie algebras.
result Key results from nilpotent Lie algebras still hold in broader settings.
Proofs centerless unimodular contact Lie algebras.
problem Characterizing centerless unimodular contact Lie algebras.
method Elementary proof and introduction of DS-contact Lie algebras.
result The only centerless unimodular examples are and .
Using technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so called quantum master equation satisfying certain boundary conditions are proven to be in 1-1 correspondence with representations of …
Constructs quaternionic complexes over unimodular quaternionic manifolds.
problem Existence and properties of quaternionic complexes on unimodular quaternionic manifolds.
method Elementary calculation and conformal invariance.
result Ellipticity and Hodge-type decomposition of quaternionic complexes.
New Einstein manifolds split into symmetric and compact parts.
problem Understanding Einstein manifolds with unimodular isometry groups.
method Theory of polar actions, Lie-theoretic arguments, and maximum principles.
result Negative Einstein manifolds split into symmetric and compact parts.
Study Riemannian Q-manifolds with Killing vector fields, finding them unimodular.
problem Defining and studying Riemannian structures on Q-manifolds.
method Define Riemannian Q-manifolds and show their unimodularity.
result Riemannian Q-manifolds are unimodular.
We construct integral bases for the SO(3)-TQFT-modules of surfaces in genus one and two at roots of unity of prime order and show that the corresponding mapping class group representations preserve a unimodular Hermitian form over a ring of algebraic integers. For higher genus surfaces the Hermitian form sometimes must…
Unimodular classification of symmetric matrix map-germs.
problem Classifying symmetric matrix map-germs under volume-preserving equivalence.
method Introducing symmetrical quasi-homogeneity and volume-preserving equivalence.
result All simple -equivalence classes coincide with volume-preserving equivalence classes.
In this paper, we investigated the behavior of left-invariant conformal vector fields on Lie groups with left-invariant pseudo-Riemannian metrics. First of all, we prove that conformal vector fields on pseudo-Riemannian unimodular Lie groups are Killing. Then we obtain a necessary condition for a pseudo-Rimennian non-u…
We study left-invariant locally conformally Kähler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex structure is bi-invariant or abelian. In the former case, we show that no such Lie algebra is uni…
Contravariant gravity on Poisson manifolds is linked to Einstein gravity.
problem Exploring the relationship between Poisson gravity and Einstein gravity.
method Investigating the compatibility of Poisson and Riemann structures to define a unique connection and derive the contravariant gravity theory.
result The contravariant gravity theory can be described as an equivalent system of Einstein gravity coupled to matter.
After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point parti…
Complete left-invariant affine structures on solvable non-unimodular three-dimensional Lie groupsmath.DG
In this paper, we shall use a method based on the theory of extensions of left-symmetric algebras to classify complete left-invariant affine real structures on solvable non-unimodular three-dimensional Lie groups.
We obtain an exhaustive classification of totally umbilical surfaces in unimodular and non-unimodular simply-connected 3-dimensional Lie groups endowed with arbitrary left-invariant Riemannian metrics. This completes the classification of totally umbilical surfaces in homogeneous Riemannian 3-manifolds.
We compute the hyperbolic covolume of the automorphism group of each even unimodular Lorentzian lattice. The result is obtained as a consequence of a previous work with Belolipetsky, which uses Prasad's volume to compute the volumes of the smallest hyperbolic arithmetic orbifolds.
A Levi-Malcev type decomposition for -step solvable Lie algebras with a complex structure
problem Decomposition of -step solvable Lie algebras with a complex structure
method Proving a Levi-Malcev type decomposition
result Fino-Vezzoni conjecture holds for -step solvable unimodular Lie algebras
Study of symmetries in 4D Lie groups.
problem Understanding symmetries in specific Lie groups.
method Analyzing isometry groups of left-invariant metrics.
result Full description of isometry groups for 4D Lie groups.
Let be a -dimensional unimodular Lie algebra equipped with a Hermitian structure such that the complex structure is abelian and the fundamental form is balanced. We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of , being the dim…
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution of structure constants of the metric Lie algebra with respect to an evolving or…
Exact G2-structures found on specific Lie algebras.
problem Finding exact G2-structures on unimodular Lie algebras.
method Examining seven-dimensional unimodular Lie algebras with vanishing third Betti number.
result No compact examples of exact G2-structures on seven-dimensional simply connected Lie groups with (2,3)-trivial Lie algebras.
Conformally covariant parametrizations for initial data in some modified Einstein gravity theoriesmath.DG
Proposes new conformal parametrizations for modified Einstein gravity.
problem Initial data in modified Einstein gravity theories.
method Proposes conformal parametrizations that lead to conformally covariant systems.
result Some conformal parametrizations give rise to conformally covariant systems.
A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this article, this canonical coframing on M is defined, its invariants are discussed and interpreted geom…
PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.
problem Characterizing and solving Finsler gravity equations.
method Analysis of Berwald spaces, -metrics, and exact solutions to Finsler gravity equations.
result Exact vacuum solutions in Finsler gravity.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…
We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand, we give an example of a solvable unimodular Lie algebra of dimension 5 that has no orthonormal geodesic basis, for any inner product.
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the defo…
We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization …
Unified theory connects local and global geometric properties of random hyperbolic polyhedra.
problem Understanding the conformal type of unimodular random infinite trivalent hyperbolic polyhedra.
method Developed a geometric and probabilistic theory using disk triangulations and circle patterns.
result Established a sharp dichotomy between parabolic and hyperbolic types based on local geometric characteristics.
We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.
We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…
Anomaly flow on Lie groups finds diverse behavior in solutions.
problem Finding solutions to the Hull-Strominger system on Lie groups.
method Examined the long-time behavior of the Anomaly flow on unimodular Lie groups.
result Diverse and intricate behavior of the Anomaly flow depends on Lie group and initial data.
Study on completeness of metrics on specific Lie groups.
problem Completeness of left-invariant Lorentzian metrics on 3D non-unimodular Lie groups.
method Analyzing metrics with Lie algebra of the form for various .
result Determine all geodesically complete and incomplete metrics for different cases of .
Ricci Flow Gravitygr-qc
A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gr…