Copertina

Principles of Locally Conformally Kähler Geometry

This monograph introduces readers to locally conformally Kähler (LCK) geometry and provides an extensive overview of the most current results. A rapidly developing area in complex geometry dealing with non-Kähler manifolds, LCK geometry has strong links to many other areas of mathematics, including...

Descrizione completa

Salvato in:
Dettagli Bibliografici
Autori principali: Ornea, Liviu (Autore), Verbitsky, Misha (Autore)
Ente Autore: SpringerLink (Online service)
Natura: Elettronico eBook
Lingua:inglese
Pubblicazione: Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.
Edizione:1st ed. 2024.
Serie:Progress in Mathematics, 354
Soggetti:
Geometry, Differential.
Algebraic geometry.
Functions of complex variables.
Differential Geometry.
Algebraic Geometry.
Several Complex Variables and Analytic Spaces.
Accesso online:https://doi.org/10.1007/978-3-031-58120-5
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
Sommario:
  • Introduction
  • Part I: Lectures in locally conformally Kähler geometry
  • Kähler manifolds
  • Connections in vector bundles and the Froebenius theorem
  • Locally conformally Kahler manifolds
  • Hodge theory on complex manifolds and Vaisman's theorem
  • Holomorphic vector bundles
  • CR, Contact and Sasakian manifolds
  • Vaisman manifolds
  • The structure of compact Vaisman manifolds
  • Orbifolds
  • Quasi-regular foliations
  • Regular and quasi-regular Vaisman manifolds
  • LCK manifolds with potential
  • Embedding LCK manifolds with potential in Hopf manifolds
  • Logarithms and algebraic cones
  • Pseudoconvex shells and LCK metrics on Hopf manifolds
  • Embedding theorem for Vaisman manifolds
  • Non-linear Hopf manifolds
  • Morse-Novikov and Bott-Chern cohomology of LCK manifolds
  • Existence of positive potentials
  • Holomorphic S^1 actions on LCK manifolds
  • Sasakian submanifolds in algebraic cones
  • Oeljeklaus-Toma manifolds
  • Appendices
  • Part II: Advanced LCK geometry
  • Non-Kähler elliptic surfaces
  • Kodaira classification for non-Kähler complex surfaces
  • Cohomology of holomorphic bundles on Hopf manifolds
  • Mall bundles and flat connections on Hopf manifolds
  • Kuranishi and Teichmüller spaces for LCK manifolds with potential
  • The set of Lee classes on LCK manifolds with potential
  • Harmonic forms on Sasakian and Vaisman manifolds
  • Dolbeault cohomology of LCK manifolds with potential
  • Calabi-Yau theorem for Vaisman manifolds
  • Holomorphic tensor fields on LCK manifolds with potential
  • Part III: Topics in locally conformally Kähler geometry
  • Twisted Hamiltonian actions and LCK reduction
  • Elliptic curves on Vaisman manifolds
  • Submersions and bimeromorphic maps of LCK manifolds
  • Bott-Chern cohomology of LCK manifolds with potential
  • Hopf surfaces in LCK manifolds with potential
  • Riemannian geometry of LCK manifolds
  • Einstein-Weyl manifolds and the Futaki invariant
  • LCK structures on homogeneous manifolds
  • LCK structures on nilmanifolds and solvmanifolds
  • Explicit LCK metrics on Inoue surfaces
  • More on Oeljeklaus-Toma manifolds
  • Locally conformally parallel and non-parallel structures
  • Open questions.

Documenti analoghi