On the groups of c-projective transformations of complete K\'ahler manifolds
| Autor: | Vladimir S. Matveev, Katharina Neusser |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Conjecture Group (mathematics) Mathematics::Complex Variables Complex projective space 010102 general mathematics Kähler manifold 01 natural sciences Differential geometry 32Q15 32J27 53A20 53C24 22F50 37J35 0103 physical sciences Metric (mathematics) 010307 mathematical physics Geometry and Topology Affine transformation Mathematics::Differential Geometry 0101 mathematics Constant (mathematics) Mathematics::Symplectic Geometry Analysis Mathematics |
| Popis: | We show that for any complete connected K\"ahler manifold the index of the group of complex affine transformations in the group of c-projective transformations is at most two unless the K\"ahler manifold is isometric to complex projective space equipped with a positive constant multiple of the Fubini-Study metric. This establishes a stronger version of the recently proved Yano-Obata conjecture for complete K\"ahler manifolds. Comment: 24 pages; a few more minor corrections; to appear in Annals of Global Analysis and Geometry |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|