%0 Journal Article %T Weil-Petersson metrics on deformation spaces %J Journal of the Iranian Mathematical Society %I Iranian Mathematical Society %Z 2717-1612 %A Cao, H.-D. %A Sun, X. %A Yau, S.-T. %A Zhang, Y. %D 2020 %\ 01/01/2020 %V 1 %N 1 %P 117-128 %! Weil-Petersson metrics on deformation spaces %K ‎Weil-Petersson metrics %K Deformation Spaces %K moduli space %R 10.30504/jims.2020.104184 %X In this paper we survey various aspects of the classical wpm and its generalizations‎, ‎in particular on the moduli space of ke manifolds‎. ‎Being a natural $L^2$ metric on the parameter space of a family of complex manifolds (or holomorphic vector bundles) which admit some canonical metrics‎, ‎the wpm is well defined when the automorphism group of each fiber is discrete and the curvature of the wpm can be computed via certain integrals over each fiber‎. ‎We shall discuss the Fano case when these fibers may have continuous automorphism groups‎. ‎We also discuss the relation between the wpm on Teichm"uller spaces of K"ahler-Einstein manifolds of general type and energy of harmonic maps‎. In this paper we survey various aspects of the classical wpm and its generalizations‎, ‎in particular on the moduli space of ke manifolds‎. ‎Being a natural $L^2$ metric on the parameter space of a family of complex manifolds (or holomorphic vector bundles) which admit some canonical metrics‎, ‎the wpm is well defined when the automorphism group of each fiber is discrete and the curvature of the wpm can be computed via certain integrals over each fiber‎. ‎We shall discuss the Fano case when these fibers may have continuous automorphism groups‎. ‎We also discuss the relation between the wpm on Teichm"uller spaces of K"ahler-Einstein manifolds of general type and energy of harmonic maps‎. %U https://jims.ims.ir/article_104184_b5c880cdd6543fe6c6b09d421a48be6a.pdf