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Normal form for pseudo-Einstein contact forms and intrinsic CR normal coordinates
We give a normal form for pseudo-Einstein contact forms and apply it to construct intrinsic CR normal coordinates parametrized by the structure group...
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Compactness of Dirac–Einstein Spin Manifolds and Horizontal Deformations
In this paper, we consider the Hilbert–Einstein–Dirac functional, whose critical points are pairs, metrics-spinors, that satisfy a system coupling...
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Weighted numerical range and weighted numerical radius for even-order tensor via Einstein product
The main aim of this article is to introduce the weighted numerical range and the weighted numerical radius for an even-order square tensor via the...
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Four-Dimensional Homogeneous Generalizations of Einstein Metrics
We review some generalizations of Einstein metrics and focus on the four-dimensional homogeneous case to exhibit classification results and new...
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Einstein-Weyl Structure and Contact Geometry
We study Einstein-Weyl structure on K -contact and contact metric manifolds satisfying certain condition on the Weyl curvature tensor and prove that...
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The time-dependent Hartree–Fock–Bogoliubov equations for Bosons
We introduce the map of dynamics of quantum Bose gases into dynamics of quasifree states, which we call the “nonlinear quasifree approximation”. We...
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Computational Problems of Einstein’s Equations
In this section, we want to point out the extreme complexity of Einstein’s equations which does not allow us to find their analytical solution of the...
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Einstein’s second-biggest blunder: the mistake in the 1936 gravitational-wave manuscript of Albert Einstein and Nathan Rosen
In a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It...
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Extended graph 4-manifolds, and Einstein metrics
We show that extended graph 4-manifolds (as defined by Frigerio–Lafont–Sisto in [
12 ]) do not support Einstein metrics. -
Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions
We study the local geometry of 4-manifolds equipped with a para-Kähler-Einstein (pKE) metric, a special type of split-signature pseudo-Riemannian...
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Existence of nontopological solutions of the self-dual Einstein-Maxwell-Higgs equations on compact surfaces
In this paper, we show the existence of nontopological solutions to the self-dual Einstein-Maxwell-Higgs equations on a compact surface when the...
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Twisting non-shearing congruences of null geodesics, almost CR structures and Einstein metrics in even dimensions
We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and...
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Toric Sasaki–Einstein metrics with conical singularities
We show that any toric Kähler cone with smooth compact cross-section admits a family of Calabi–Yau cone metrics with conical singularities along its...
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A Class of Einstein Submanifolds of Euclidean Space
In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for...
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Multiple Higher-Order Pole Solutions in Spinor Bose–Einstein Condensates
In this study, multiple higher-order pole solutions of spinor Bose–Einstein condensates are explored by means of the inverse scattering transform,...
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2nd order approximate Noether and Lie symmetries of Gibbons–Maeda–Garfinkle–Horowitz–Strominger charged black hole in the Einstein frame
In this paper, approximate Noether and Lie symmetries of 2nd order for Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) charged black hole in the...
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Balance Equations
Borrowing from the mechanics of systems of particles, the balance equations for mass, linear momentum, and angular momentum are established. Next,...