On some variational problems for 2-dimensional Hermitian metrics

✍ Scribed by Izu Vaisman

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 328 KB
• Volume: 8
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00127999

✦ Synopsis

Let (M, J, g) be a compact complex 2-dimensional Hermitian manifold with the Kahler form 2, and the torsion 1-form co defined by dQ = c A 2. In this note we obtain the Euler-Lagrange equations for the variational functionals defined by 11coll 2 and Ildcoll2, where g runs in the space of all the Hermitian metrics on M. In the first case, the extremals are precisely the Kihler metrics [Gd]. In the second case, we also write down a formula for the second variation. * = -LCT, *dT = -C d -(C + *) A (X A do).