The Einstein-Hilbert action of the space of holomorphic maps from S2 to CPk

JOURNAL OF GEOMETRY AND PHYSICS

卷:74

Article

Alqahtani, L. S.

关键词: Einstein Hilbert action;    Holomorphic maps;    2-sphere;    Complex projective space;   

DOI  :  10.1016/j.geomphys.2013.07.010

来源: Elsevier

【 摘 要 】

Let H-n.k(Sigma) be the space of degree n > 1 holomorphic maps from a compact Riemann surface Sigma to CPk. In the case E = S-2 and n = 1, the L-2 metric on H-1,H-k (S-2) was computed exactly by Speight. In this paper, the Ricci curvature tensor and the scalar curvature on Rik(S-2) are determined explicitly for k > 2. An exact direct computation of the Einstein Hilbert action with respect to the L-2 metric on H-1,H-k(s(2)) is made and shown to coincide with a formula conjectured by Baptista. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free