My current research has brought me into an area the requires me to learn some infinite dimensional Riemannian and Kähler geometry. Can someone recommend some good books or survey articles to help me get started with the basics? I've seen Lang's book but that's it.



Infinite dimensional Riemannian geometry
Lempert, László The Dolbeault complex in infinite dimensions. III. Sheaf cohomology in Banach spaces. Invent. Math. 142 (2000), no. 3, 579-603.


Lempert, László The Dolbeault complex in infinite dimensions. II. J. Amer. Math. Soc. 12 (1999), no. 3, 775-793. 


Lempert, László The Dolbeault complex in infinite dimensions. I. J. Amer. Math. Soc. 11 (1998), no. 3, 485-520. 


Hamilton, Richard S. The inverse function theorem of Nash and Moser. Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 65–222. 


