Extremal Kaehler metrics and Ray-Singer analytic torsion
| dc.creator | Mueller, Werner | |
| dc.creator | Wendland, Katrin | |
| dc.date | 1999-04-12 | |
| dc.date | 1999-05-06 | |
| dc.date.accessioned | 2026-07-07T05:28:39Z | |
| dc.date.available | 2026-07-07T05:28:39Z | |
| dc.description | Let (X,[ω]) be a compact Kaehler manifold with a fixed Kaehler class [ω]. Let K_ωbe the set of all Kaehler metrics on X whose Kaehler class equals [ω]. In this paper we investigate the critical points of the functional Q(g)= |v|_g T_0(X,g)^{1/2} for g \in K_ω, where v is a fixed nonzero vector of the determinant line λ(X) associated to H^*(X) and T_0(X,g) is the Ray-Singer analytic torsion. For a polarized algebraic manifold (X,L) we consider a twisted version Q_L(g) of this functional and assume that c_1(L)=[ω]. Then the critical points of Q_L are exactly the metrics g\in K_ωof constant scalar curvature. In particular, if c_1(X)=0 or if c_1(X)<0 and 1/(2π)[ω] = -c_1(X), then K_ωcontains a unique Kaehler-Einstein metric g_{KE} and Q_L attains its absolut maximum at g_{KE}. | |
| dc.description | 33 pages, LaTeX2e, to be published in Geometric Aspects of partial differential equations, Proceedings of the Roskilde Conference, Sept. 1998, AMS series Contemporary Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/9904048 | |
| dc.identifier | http://arxiv.org/abs/math/9904048 | |
| dc.identifier | Geometric aspects of partial differential equations (Roskilde, 1998), 135--160, Contemp. Math., 242, Amer. Math. Soc., Providence, RI, 1999 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78342 | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 58G26 (Primary) 58E11, 53C55 (Secondary) | |
| dc.title | Extremal Kaehler metrics and Ray-Singer analytic torsion | |
| dc.type | text |