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Critical metrics of the total scalar curvature functional on 4-manifolds [PDF]
Mathematische Nachrichten, 2015 The purpose of this paper is to investigate the critical points of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume, for simplicity CPE metrics. It was conjectured in $1980$'s that every CPE metric must be Einstein. We prove that a $4$-dimensional CPE metric with harmonic tensor $W^+$
A. Barros, B. Leandro, E. Ribeiro
exaly +6 more sources
Deformation of Scalar Curvature and Volume
Mathematische Annalen, 2013 The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics.
Corvino, Justin +2 more
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On the decoherence of primordial gravitons
Journal of High Energy Physics, 2023 It is well-known that the primordial scalar curvature and tensor perturbations, ζ and γ ij , are conserved on super-horizon scales in minimal inflation models. However, their wave functional has a rapidly oscillating phase which is slow-roll unsuppressed,
Sirui Ning, Chon Man Sou, Yi Wang
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Weyl type f(Q, T) gravity, and its cosmological implications
European Physical Journal C: Particles and Fields, 2020 We consider an f(Q, T) type gravity model in which the scalar non-metricity $$Q_{\alpha \mu \nu }$$ Qαμν of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $$w_{\mu }$$ wμ .
Yixin Xu +3 more
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Polynomial Hamiltonian form of General Relativity [PDF]
, 2005 Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial form.
A. Ashtekar +21 more
core +4 more sources
Behavior of Quasilocal Mass Under Conformal Transformations [PDF]
, 1998 We show that in a generic scalar-tensor theory of gravity, the ``referenced'' quasilocal mass of a spatially bounded region in a classical solution is invariant under conformal transformations of the spacetime metric.
A. D. Popova +30 more
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Perelman's Invariant, Ricci Flow, and the Yamabe Invariants of Smooth Manifolds [PDF]
, 2006 In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called lambda-bar. We show here that, for completely elementary reasons, this invariant simply equals the Yamabe invariant, alias the sigma constant, whenever the latter is non ...
Akutagawa, Kazuo +2 more
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Scaling Behaviour of Conformal Fields in Curved Three-dimensional Space [PDF]
, 1998 The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field.
Tsoupros, George
core +4 more sources
Curvature in Noncommutative Geometry
, 2020 Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past ten years. This new episode in noncommutative geometry started when a Gauss-Bonnet theorem was proved by Connes and Tretkoff for a curved ...
A Buium +32 more
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Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance [PDF]
, 2004 A covariant approach towards a theory of deformations is developed to examine both the first and second variation of the Helfrich-Canham Hamiltonian -- quadratic in the extrinsic curvature -- which describes fluid vesicles at mesoscopic scales ...
Bo?i? B +22 more
core +2 more sources