English

Principles of Locally Conformally Kahler Geometry

Differential Geometry 2024-12-10 v6 Algebraic Geometry Complex Variables

Abstract

An LCK (locally conformally Kahler) manifold is a complex manifold admitting a Kahler covering with monodromy acting by homotheties. Hopf manifolds and their submanifolds are the prime examples. This book presents an introduction to the principles of LCK geometry (the first two parts) and its current situation (the last part). It is supposed to be accessible to master and graduate students of complex geometry. The book contains many exercises of different levels of difficulty. We finish it by a list of open questions.

Keywords

Cite

@article{arxiv.2208.07188,
  title  = {Principles of Locally Conformally Kahler Geometry},
  author = {Liviu Ornea and Misha Verbitsky},
  journal= {arXiv preprint arXiv:2208.07188},
  year   = {2024}
}

Comments

754 pages, 14 figures, version 6.0, Latex. Many misprints corrected, thanks to Ethan Addison. The Birkh\"auser publication is available at https://link.springer.com/book/9783031581199