Existence criteria for special locally conformally Kähler metrics

Clicks: 74
ID: 117756
2018
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Emerging

Ranked #16 of 17 articles by views in annali di matematica pura ed applicata (1923 -)

Most read Least read

Bar heights use a square-root scale.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
We investigate the relation between holomorphic torus actions on complex manifolds of locally conformally Kähler (LCK) type and the existence of special LCK metrics. We show that if the group of biholomorphisms of such a manifold (M, J) contains a compact torus which is not totally real, then there exists a Vaisman metric on the manifold, generalising a result of Kamishima–Ornea. Also, we obtain a new obstruction to the existence of LCK structures on a given complex manifold in terms of its automorphism group. As an application, we obtain a classification of manifolds of LCK type among all the manifolds having the structure of a holomorphic principal torus bundle. Moreover, we show that if the group of biholomorphisms contains a compact torus whose dimension is half the real dimension of M, then (M, J) admits an LCK metric with positive potential. Finally, we obtain new non-existence results for LCK metrics on certain products of complex manifolds.
Reference Key
istrati2018annaliexistence Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Nicolina Istrati;Nicolina Istrati;
Journal annali di matematica pura ed applicata (1923 -)
Year 2018
DOI
doi:10.1007/s10231-018-0776-2
URL
https://link.springer.com/article/10.1007/s10231-018-0776-2
Keywords
mathematics general

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.