English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We show that the Einstein–Hilbert functional, as a functional on the space of Reeb vector fields, detects the vanishing Sasaki–Futaki invariant. In particular, this provides an obstruction to the existence of a constant scalar curvature Sasakian metric. As an application we prove that K-semistable polarized Sasaki manifold has vanishing Sasaki–Futaki invariant. We then apply this result to show that under the right conditions on the Sasaki join manifolds of [ 6 ], a polarized Sasaki manifold admits constant scalar curvature Sasaki metric if it is K-polystable.

The Einstein–Hilbert Functional and the Sasaki–Futaki Invariant