Displaying similar documents to “Einstein Structures: Existence Versus Uniqueness.”

4-dimensional anti-Kähler manifolds and Weyl curvature

Jaeman Kim (2006)

Czechoslovak Mathematical Journal

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On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.

Weakly-Einstein hermitian surfaces

Vestislav Apostolov, Oleg Muškarov (1999)

Annales de l'institut Fourier

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A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as we obtain a complete classification of the compact locally homogeneous * -Einstein Hermitian surfaces. We also provide large families of non-homogeneous * -Einstein (but non-Einstein) Hermitian metrics on ℂ ℙ 2 ♯ ℂ ℙ ‾ 2 , ℂ ℙ 1 × ℂ ℙ 1 , and on the product surface X × Y of two curves X and Y whose genuses are greater than 1...

Hermitian curvature flow

Jeffrey Streets, Gang Tian (2011)

Journal of the European Mathematical Society

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We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein...

Renormalized volume and the evolution of APEs

Eric Bahuaud, Rafe Mazzeo, Eric Woolgar (2015)

Geometric Flows

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We study the evolution of the renormalized volume functional for even-dimensional asymptotically Poincaré-Einstein metrics (M, g) under normalized Ricci flow. In particular, we prove that [...] where S(g(t)) is the scalar curvature for the evolving metric g(t). This implies that if S +n(n − 1) ≥ 0 at t = 0, then RenV(Mn , g(t)) decreases monotonically. For odd-dimensional asymptotically Poincaré-Einstein metrics with vanishing obstruction tensor,we find that the conformal anomaly for...