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Conformally flat FRW metrics  [PDF]
Masao Iihoshi,Sergei V. Ketov,Atsushi Morishita
Physics , 2007, DOI: 10.1143/PTP.118.475
Abstract: We find a new family of non-separable coordinate transformations bringing the FRW metrics into the manifestly conformally flat form. Our results are simple and complete, while our derivation is quite explicit. We also calculate all the FRW curvatures, including the Weyl tensor.
All conformally flat pure radiation metrics  [PDF]
S. Brian Edgar,Garry Ludwig
Physics , 1996, DOI: 10.1088/0264-9381/14/4/001
Abstract: The complete class of conformally flat, pure radiation metrics is given, generalising the metric recently given by Wils.
Einstein and conformally flat critical metrics of the volume functional  [PDF]
Pengzi Miao,Luen-Fai Tam
Mathematics , 2009,
Abstract: Let $R$ be a constant. Let $\mathcal{M}^R_\gamma$ be the space of smooth metrics $g$ on a given compact manifold $\Omega^n$ ($n\ge 3$) with smooth boundary $\Sigma $ such that $g$ has constant scalar curvature $R$ and $g|_{\Sigma}$ is a fixed metric $\gamma$ on $\Sigma$. Let $V(g)$ be the volume of $g\in\mathcal{M}^R_\gamma$. In this work, we classify all Einstein or conformally flat metrics which are critical points of $V(\cdot)$ in $\mathcal{M}^R_\gamma$.
Comment on "Conformally flat stationary axisymmetric metrics"  [PDF]
Alan Barnes,Jose MM Senovilla
Physics , 2003, DOI: 10.1103/PhysRevD.68.049901
Abstract: Garcia and Campuzano claim to have found a previously overlooked family of stationary and axisymmetric conformally flat spacetimes, contradicting an old theorem of Collinson. In both these papers it is tacitly assumed that the isometry group is orthogonally transitive. Under the same assumption, we point out here that Collinson's result still holds if one demands the existence of an axis of symmetry on which the axial Killing vector vanishes. On the other hand if the assumption of orthogonal transitivity is dropped, a wider class of metrics is allowed and it is possible to find explicit counterexamples to Collinson's result.
Compactness for conformal metrics with Constant $Q$ curvature on locally conformally flat manifolds  [PDF]
Jie Qing,David Raske
Mathematics , 2005,
Abstract: In this note we study the conformal metrics of constant $Q$ curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension $n\geq 5$ and with Poincar\"{e} exponent less than $\frac {n-4}2$, the set of conformal metrics of positive constant $Q$ and positive scalar curvature is compact in the $C^\infty$ topology.
Conformally flat metrics on 4-manifolds  [PDF]
Michael Kapovich
Mathematics , 2002,
Abstract: We prove that for each closed smooth spin 4-manifold M there exists a closed smooth 4-manifold N such that the connected sum M # N admits a conformally flat Riemannian metric.
Integration using invariant operators:Conformally flat radiation metrics  [PDF]
S. B. Edgar,J. A. Vickers
Physics , 1998, DOI: 10.1088/0264-9381/16/2/020
Abstract: A new method is presented for obtaining the general conformally flat radiation metric by using the differential operators of Machado Ramos and Vickers (a generalisation of the GHP operators) which are invariant under null rotations and spin and boosts. The solution is found by constructing involutive tables of these derivatives applied to the quantities which arise in the Karlhede classification of metrics.
Conformally flat pencils of metrics, Frobenius structures and a modified Saito construction  [PDF]
Liana David,Ian A. B. Strachan
Physics , 2005, DOI: 10.1016/j.geomphys.2005.08.003
Abstract: The structure of a Frobenius manifold encodes the geometry associated with a flat pencil of metrics. However, as shown in the authors' earlier work, much of the structure comes from the compatibility properties of the pencil rather than from the flatness of the pencil itself. In this paper conformally flat pencils of metrics are studied and examples, based on a modification of the Saito construction, are studied.
CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics  [PDF]
Xiaojun Huang,Shanyu Ji,Brandon Lee
Mathematics , 2012,
Abstract: We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also study rigidity problems for conformal maps between a class of K\"ahler manifolds with pseud-conformally flat metrics.
On conformally flat and type N pure radiation metrics  [PDF]
Jiri Podolsky,Ondrej Prikryl
Physics , 2008, DOI: 10.1007/s10714-008-0692-7
Abstract: We study pure radiation spacetimes of algebraic types O and N with a possible cosmological constant. In particular, we present explicit transformations which put these metrics, that were recently re-derived by Edgar, Vickers and Machado Ramos, into a general Ozsvath-Robinson-Rozga form. By putting all such metrics into the unified coordinate system we confirm that their derivation based on the GIF formalism is correct. We identify only few trivial differences.
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