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

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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