A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We solve linear equations with tensors of any rank.
New method solves tensor equations including parity odd and even terms in 4D.
Equations link metrics with tensors, revealing curvature constraints.
Researchers solve metric curvature equations on manifolds with boundary.
New method combines Monte Carlo and tensor networks for solving complex equations.
Solves a Monge-Ampère type equation for Nakano positive curvature tensors of holomorphic vector bundles.
The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any manifold equipped with an affine connection, and in this setting derive its prolo…
In this paper is considered the differential equation Ric(g)=T, where Ric(g) is the Ricci tensor of the metric g and T is a rotational symmetric tensor on R^n. A new, geometric, proof of the existence of smooth solutions of this equation, based on qualitative theory of implicitdifferential equations, is presented here.…
We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor to be a constant. It is related to the notion of minimal volumes in comparison geometry. Such a metric with the smallest eigenvalue of the Ricci tensor to be a constant is an extremal metric of volume in…
Develops path integral for spiked tensor model dynamics.
We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abeli…
Carter tensor analysis aids wave equation on Kerr-Newman spacetime.
Develops a formalism for studying general horizons and derives a near-horizon equation.
Study of hypersurfaces in curved spaces with specific curvature properties.
The paper defines and studies the geometric mean for tensors and its associated Riemannian geometry.
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial dif…
In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in .
The paper generalizes Bach and Einstein equations with a field.
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the notion of Killing spinors. The solutions of this spinorial field equation are c…
We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence (namely, the spatial metric tensor, the extrinsic curvature tensor and the Riema…
Characterizes conformal Killing tensors and their Killing scales.
Study spherical doubly warped spacetimes for stellar collapse and cosmology.
Study homogenizes equations on parallelizable manifolds using tensor localization and periodicity.
Signature tensors uniquely identify ODE solutions.
The paper studies hyperbolic equations in a spacetime foliation, proving existence and uniqueness.
Tensor trains simplify solving complex PDEs efficiently.
We compute all 2-covariant tensors naturally constructed from a semiriemannian metric which are divergence-free and have weight greater than -2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian met…
A new tensor completion method using tensor networks with Tucker wrapper.
We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. …
The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein-Weyl (pEW) equation. In 2-dimensions, we give local obstructions …
New method uses TT approximations to solve HJB equations for efficient sampling.
We exploit four-dimensional tensor identities to give a very simple proof of the existence of a Lanczos potential for a Weyl tensor in four dimensions with any signature, and to show that the potential satisfies a simple linear second order differential equation, e.g., a wave equation in Lorentz signature. Furthermore,…
This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov's classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.
Generalizes O'Neill's equations to pseudo-Finsler submersions.
Einstein's equation, in its standard form, breaks down at the Big Bang singularity. A new version, equivalent to Einstein's whenever the latter is defined, but applicable in wider situations, is proposed. The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model. It is…
The study finds conditions for a third rank Killing tensor field on a 2D Riemannian torus.
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic…
Efficiently samples complex distributions using tensor train format.
In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete Einstein-type manifold with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature is locally a warped product with -dimensional…
Study isotropic solutions in smooth metric measure spaces with vacuum Einstein equations.
SyGlasso models tensor data dependencies using Sylvester equations.
Paper identifies tensor ranks via prior predictive matching, solving system of equations.
We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the Nijenhuis integrability conditions for a Killing tensor into purely algebraic integra…
Proves well-posedness for Einstein equations with specific boundary data.
Killing tensor fields have been thought of as describing hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Many problems in classical mechanics can be formulated as geodesic problems in curved spaces and spacetimes, and thus solving the de…
Study proves structure results for homogeneous spaces supporting specific equations.
Study of conformally compact metrics and Lovelock tensors in even dimensions.