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On the Geometry of SasakianEinstein 5Manifolds
 MATH. ANN
"... On simply connected five manifolds SasakianEinstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollar [DK] a ..."
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Cited by 33 (16 self)
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On simply connected five manifolds SasakianEinstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollar [DK] and Johnson and Kollar [JK1] who give methods for constructing KahlerEinstein metrics on log del Pezzo surfaces. By [BG1] circle Vbundles over log del Pezzo surfaces with KahlerEinstein metrics have SasakianEinstein metrics on the total space of the bundle. Here these simply connected 5manifolds arise as links of isolated hypersurface singularities which by the well known work of Smale [Sm] together with [BG3] must be diffeomorphic to S 5
On the Geometry of SasakianEinstein
, 2001
"... Abstract: On simply connected five manifolds SasakianEinstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kol ..."
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Abstract: On simply connected five manifolds SasakianEinstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollár [DK] and Johnson and Kollár [JK1] who give methods for constructing KählerEinstein metrics on log del Pezzo surfaces. By [BG1] circle Vbundles over log del Pezzo surfaces with KählerEinstein metrics have SasakianEinstein metrics on the total space of the bundle. Here these simply connected 5manifolds arise as links of isolated hypersurface singularities which by the well known work of Smale [Sm] together with [BG3] must be diffeomorphic to S 5 #l(S 2 ×S 3). More precisely, using methods from Mori theory in algebraic geometry we prove the existence of 14 inequivalent SasakianEinstein structures on S 2 ×S 3 and infinite families of such structures on #l(S 2 ×S 3) with 2≤l≤7. We also discuss the moduli problem for these SasakianEinstein structures. Surprisingly little is known about complete Einstein metrics on compact 5manifolds. Until now one could list only two constructions of such metrics. The more recent one was
Kähler Ricci Flow on Fano Manifolds (I)
, 2009
"... We study the evolution of anticanonical line bundles along the Kähler Ricci flow. We show that under some conditions, the convergence of Kähler Ricci flow is determined by the properties of the anticanonical divisors of M. As examples, the Kähler Ricci flow on M converges when M is a Fano surface an ..."
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We study the evolution of anticanonical line bundles along the Kähler Ricci flow. We show that under some conditions, the convergence of Kähler Ricci flow is determined by the properties of the anticanonical divisors of M. As examples, the Kähler Ricci flow on M converges when M is a Fano surface and c2 1 (M) = 1 or c21 (M) = 3. Combined with the work in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups. The original proof of