Results 1 to 10 of about 29,727 (93)
Critical point equation on almost f-cosymplectic manifolds [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers.
H. Aruna Kumara +2 more
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Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds [PDF]
Colloquium Mathematicum, 2022 Summary: We study rigidity of critical metrics for quadratic curvature functions \(\mathcal{F}_{t,s}(g)\) involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor. In particular, when \(s=0\), we give new characterizations by pointwise inequalities involving the Weyl curvature and the traceless Ricci tensor for critical ...
Ma, Bingqing, Huang, Guangyue
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Constitutive tensor in the geometrized Maxwell theory
Discrete and Continuous Models and Applied Computational Science, 2022 It is generally accepted that the main obstacle to the application of Riemannian geometrization of Maxwell’s equations is an insufficient number of parameters defining a geometrized medium. In the classical description of the equations of electrodynamics
Anna V. Korolkova
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Information-Theoretic Models for Physical Observables
Entropy, 2023 This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular ...
D. Bernal-Casas, J. M. Oller
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Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds
Advances in Mathematics, 2007 We consider the moduli space of the extremal K hler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can be compactified by including (reduced) orbifolds with finitely many singularities.
Chen, Xiuxiong, Weber, Brian
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Causal continuity in degenerate spacetimes [PDF]
, 1999 A change of spatial topology in a causal, compact spacetime cannot occur when the metric is globally Lorentzian. One can however construct a causal metric from a Riemannian metric and a Morse function on the background cobordism manifold, which is ...
+35 more
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A spinorial energy functional: critical points and gradient flow [PDF]
, 2015 On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}.
A Besse +39 more
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Some rigidity results on critical metrics for quadratic functionals [PDF]
, 2014 In this paper we prove rigidity results on critical metrics for quadratic curvature functionals, involving the Ricci and the scalar curvature, on the space of Riemannian metrics with unit volume. It is well-known that Einstein metrics are always critical
Catino, Giovanni
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Conformal Spectrum and Harmonic maps [PDF]
, 2014 This paper is devoted to the study of the conformal spectrum (and more precisely the first eigenvalue) of the Laplace-Beltrami operator on a smooth connected compact Riemannian surface without boundary, endowed with a conformal class.
Nadirashvili, Nikolai, Sire, Yannick
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Generic Properties of Critical Points of the Weyl Tensor
Advanced Nonlinear Studies, 2017 Given (M,g)${(M,g)}$, a smooth compact Riemannian n-manifold, we prove that for a generic Riemannian metric g the critical points of the function 𝒲g(ξ):=|Weylg(ξ)|g2${\mathcal{W}_{g}(\xi):=\lvert\mathrm{Weyl}_{g}(\xi)\rvert^{2}_{g}}$ with 𝒲g(ξ)≠0 ...
Micheletti Anna Maria, Pistoia Angela
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