Communications in Analysis and Geometry

Volume 25 (2017)

Number 3

Holomorphic automorphisms of the loop space of $\mathbb{P}^n$

Pages: 709 – 718



Ning Zhang (School of Mathematical Sciences, Peking University, Beijing, China; and School of Mathematical Sciences, Ocean University of China, Qingdao, China)


The loop space $L \mathbb{P}^n$ of the complex projective space $\mathbb{P}^n$ consisting of all $C^k$ or Sobolev $W^{k,p}$ maps $S^1 \to \mathbb{P}^n$ is an infinite dimensional complex manifold. We identify a class of holomorphic self-maps of $L \mathbb{P}^n$, including all automorphisms.


loop space, holomorphic self-map, automorphism group, projective space

2010 Mathematics Subject Classification

32H02, 46G20, 58B12, 58C10, 58D15

The author’s research was partially supported by the National Natural Science Foundation of China grant 10871002.

Received 21 September 2012

Published 13 September 2017