We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor.
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48 results for “Wick-rotated metric”
We study Wick-rotations of left-invariant metrics on Lie groups, using results from real GIT (\cite{1}, \cite{2}, \cite{3}). An invariant for Wick-rotation of Lie groups is given, and we describe when a pseudo-Riemannian Lie group can be Wick-rotated to a Riemannian Lie group. We also prove a general version (for gener…
Paper introduces a new cosmological volume function and its properties.
problem Introducing a new cosmological volume function.
method Introduces and analyzes the cosmological volume function τ_V, showing it's continuously differentiable.
result τ_V leads to a canonical splitting of the metric tensor and a canonical Wick-rotated Riemannian metric.
Motivated by Wick-rotations of pseudo-Riemannian manifolds, we study real geometric invariant theory (GIT) and compatible representations. We extend some of the results from earlier works \cite{W2,W1}, in particular, we give some sufficient as well as necessary conditions for when pseudo-Riemannian manifolds are Wick-r…
Wick rotations and real GITmath.DG
We define Wick-rotations by considering pseudo-Riemannian manifolds as real slices of a holomorphic Riemannian manifold. From a frame bundle viewpoint Wick-rotations between different pseudo-Riemannian spaces can then be studied through their structure groups which are real forms of the corresponding complexified Lie g…
In this paper we investigate relations between solutions to the minimal surface equation in Euclidean -space , the zero mean curvature equation in Lorentz-Minkowski -space and the Born-Infeld equation under Wick rotations. We prove that the existence conditions of real solutions and i…
Given a closed hyperbolic surface , let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-de Sitter metrics on . We describe natural maps between (parts of) $\cQF$ and $\cGH_{-1}$, called "Wick rotations", defined in te…
We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete Cauchy surface (in particular a compact one), as well as complex projective str…
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…
The paper shows how Scherk-type surfaces can be decomposed into helicoids.
problem Decomposing Scherk-type zero mean curvature surfaces.
method Using a special Euler-Ramanujan identity and Wick rotation, the paper expresses these surfaces as an infinite superposition of dilated helicoids and provides different finite decompositions.
result Scherk-type zero mean curvature surfaces can be expressed as an infinite superposition of dilated helicoids.
The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.
problem Understanding composition of Lagrangian correspondences in Hilbert spaces.
method Study of Lagrangian correspondences, construction of a category, and functorial field theory.
result Well-defined composition law in a category of Lagrangian correspondences.
Gravitational Solitons and Complete Ricci Flat Riemannian Manifolds of Infinite Topological Typemath.DG
New gravitational solitons and infinite topological manifolds found.
problem Finding new gravitational solitons and Riemannian manifolds.
method Space-periodic solutions of Einstein equations, quotients, Wick rotation.
result Complete Ricci flat Riemannian manifolds of infinite topological type.
Quantum mechanics models for financial Black-Scholes model.
problem Modeling financial derivatives using quantum mechanics.
method Noncommutative quantum mechanics applied to specific mechanical systems.
result Generalized noncommutative quantum mechanics of financial models.
Quantum method prices options by evolving a state in imaginary time.
problem Pricing options in a quantum setting.
method Prepares an initial state, evolves it using imaginary time algorithms, and maps to quantum state.
result Numerical verification for European options; extension to path-dependent options.
The study finds obstructions to certain Riemannian metrics using Lorentzian geometry.
problem Finding obstructions to curvature distinguished Riemannian metrics.
method Dual Lorentzian metrics and Penrose's plane wave limit.
result Necessary local conditions for certain Riemannian metrics.
Exploring distance functions on spacetime models.
problem No canonical distance function exists for Lorentzian manifolds.
method Comparing Riemannianization and null distance function approaches.
result Concrete comparison of distance functions in GRW setting.
We obtain the Weierstrass-Enneper representation for maximal graphs(whose Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of Barbishov and Chernikov, which they have used to find the solutions of Born-Infeld equation in hodographic coordinates. We could use their method in our case, because…
In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely---taking into account that the conjecture lacks any precise formulation yet---first we make sense of what one would mean by a "generic counterexample" by introducing the mathematically unambigous and logically st…
Homogeneous M2 dualshep-th
Motivated by the search for new gravity duals to M2 branes with supersymmetry --- equivalently, M-theory backgrounds with Killing superalgebra for --- we classify homogeneous M-theory backgrounds with symmetry Lie algebra for . We f…
We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine generators for the 12-dimensional bordism group of pin manifolds with a w_1-twisted integer lift of w_4; these are the manifolds on which Wick-rotated M-theory exists. The anoma…
Study of convergence in Lorentzian spacetimes using temporal functions.
problem Non-compactness of spacetime isometries and convergence in semi-Riemannian settings.
method Introduced anchored convergence and used Cauchy temporal functions to define convergence for spacetimes.
result Established local and global regularity of Cauchy temporal functions and their properties.
The paper extends graph embedding models to handle multiple relations.
problem Link prediction in multi-relational networks.
method Generalized pseudo-Riemannian embedding models to multi-relational networks, considering relations as submanifolds.
result Validation of the approach in link prediction tasks, including knowledge graph completion and biological domain analysis.
Study large N oscillations in 3D theories related to black hole physics.
problem Understanding large N sign oscillations in 3D theories via holography.
method Holographic computation of on-shell actions for Euclidean supergravity solutions, Wick rotation of magnetically charged AdS4 black holes.
result Proposed a non-trivial mathematical conjecture regarding phase factors of twisted Reidemeister-Ray-Singer torsion.
This paper is dedicated to Oleg Viro on his 60-th birthday. The paper is about Khovanov homology and its relationships with statistical mechanics models such as the Ising model and the Potts model. We give a relatively self-contained introduction to Khovanov homology, and also a reformulation of the Potts model in term…
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite type case of the canonicla Wick rotation-rescaling theory, previously developed b…
Survey on the Canonical Metrics on the Teichmüller Spaces and the Moduli Spaces of Riemann Surfacesmath.DG
This thesis surveys various metrics on Riemann surface spaces.
problem Various metrics on Riemann surface spaces.
method Survey of metrics and their properties.
result Equivalence of Kähler-Einstein metric to Teichmüller metric.
The Weighted Ambient Metricmath.DG
Proves existence and uniqueness of weighted metrics for smooth spaces.
problem Existence and uniqueness of weighted metrics for smooth metric measure spaces.
method Proves existence and uniqueness using weighted ambient metrics and Poincaré metrics.
result Existence and uniqueness of weighted metrics for smooth metric measure spaces.
New Finsler metrics constructed from -metrics.
problem Exploring new Finsler metrics within the -metric class.
method Constructing new sub-classes of -metrics.
result Presented illustrative examples of new Finsler metrics.
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Rand…
We prove the equivalences of several classical complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new Kähler metrics, the Ricci metric and the perturbed Ricci metric and prove that the perturbed Ricci metric is a complete Kähler metric with bounded negative holomorphic s…
New metric defined for bounded symmetric domains.
problem Defining a new metric for bounded symmetric domains.
method Using generalized Hilbert metric and Borel embedding.
result The new metric differs from Carathéodory and Bergman metrics except for complex hyperbolic space.
Introduces Finslerian convolution metrics and their properties.
problem No specific problem stated; focuses on new metric concept.
method Definition and study of Finslerian convolution metrics.
result Characterization of Finslerian convolution metrics of Riemannian, Minkowskian, and Randers types.
Survey of recent metric geometry in Kähler metrics space.
problem Understanding the metric geometry of Kähler metrics space.
method Survey and highlighting of recent results.
result Highlighting of open problems in the field.
Study on geodesics of Finsler metrics derived from Riemannian metrics.
problem Investigating geodesics in Finsler metrics derived from Riemannian metrics.
method Proved geodesic lemma for a family of Riemannian geodesic orbit metrics, analyzed geodesic graphs.
result Derived Finsler metrics have geodesic orbit property and belong to a new class of metrics.
We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the space of Kähler metrics to the space of Riemannian metrics, and we study its geome…
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
problem Existence of extremal Kähler metrics on Fano manifolds.
method Introducing -extremal Kähler metrics and relating them to multiplier Hermitian-Einstein metrics.
result Existence of -extremal Kähler metrics implies existence of multiplier Hermitian-Einstein metrics on Fano manifolds.
We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then discuss a comparison theorem between it and the Calabi metric. As geometric motivati…
On -metricsmath.DG
New Finsler metrics defined by Riemannian and 1-forms are studied.
problem Characterize and study properties of -metrics.
method Introduced and defined -metrics, analyzed their properties, and found conditions for local projective flatness and Douglas type.
result Necessary and sufficient conditions for -metrics to be locally projectively flat and Douglas type were found.
Sharp estimates for Finsler metrics in convex domains.
problem Estimating distances in Finsler metrics near convex points.
method Sharp estimates for intrinsic distances of Finsler metrics.
result Characterization of -quasi hyperbolic metric in convex geometry.
Study on special Finsler metrics with conditions for Riemannian and isotropic properties.
problem Characterizing Finsler metrics with specific geometric properties.
method Analyzing conditions for Riemannian and isotropic properties of AR-Finsler metrics.
result Conditions for isotropic -curvature and mean Landsberg curvature leading to vanishing curvature.
Lee metrics on groupsmath.GR
The study examines Lee metrics on groups and their properties.
problem Characterizing groups that admit Lee metrics.
method Analyzing conditions for groups to have or not have Lee metrics, studying specific families of groups, and providing tables for groups of order ≤ 31.
result Conditions for groups to have Lee metrics, including specific families and non-cyclic groups.
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
Study shows convergence of Lagrangian submanifolds under certain metrics.
problem Understanding convergence of Lagrangian submanifolds under specific metrics.
method Proves convergence to an embedded Lagrangian submanifold using a monotonicity lemma applied on a carefully-chosen metric ball.
result Convergence to an embedded Lagrangian submanifold implies convergence in the Hausdorff metric for a class of metrics.
On Einstein square metricsmath.DG
In this paper, we study an important class of Finsler metrics--square metrics. We give two expressions of such metrics in terms of a Riemannian metric and a 1-form. We show that Einstein square metrics can be classified up to the classification of Einstein Riemannian metrics.
Defines a new Randers metric based on an existing one.
problem No specific problem stated; focuses on defining a new metric.
method Defines a new left-invariant Randers metric based on an existing one .
result Shows that is of Berwald (Douglas) type if and only if is of Berwald (Douglas) type.
Study Kähler-Einstein metrics on singular varieties, proving metric completion properties.
problem Kähler-Einstein metrics on singular projective varieties.
method Approximation with constant scalar curvature metrics, RCD space analysis.
result Metric completion of smooth part is non-collapsed RCD space and homeomorphic to original variety.
Investigates O(n)-invariant metrics on SPD matrices, extending kernel metrics.
problem Limited coverage of O(n)-invariant metrics by kernel metrics.
method Characterization of O(n)-invariant metrics, intermediate classes construction.
result Introduction of cometric-stability as a key property for geodesics.
The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with general…