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 Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

An octonionic contact (OC) manifold is always spherical. We construct the OCYamabe operator on an OC manifold and prove its transformation formula underconformal OC transformations. An OC manifold is scalar positive, negative orvanishing if and only if its OC Yamabe invariant is positive, negative or zero,respectively. On a scalar positive OC manifold, we can construct the Greenfunction of the OC Yamabe operator, and apply it to construct a conformallyinvariant tensor. It becomes an OC metric if the OC positive mass conjecture istrue. We also show the connected sum of two scalar positive OC manifolds to bescalar positive if the neck is sufficiently long. On the OC manifoldconstructed from a convex cocompact subgroup of ${\rm F}_{4(-20)}$, weconstruct a Nayatani type Carnot-Carath\'eodory metric. As a corollary, such anOC manifold is scalar positive, negative or vanishing if and only if thePoincar\'e critical exponent of the subgroup is less than, greater than orequal to $10,$ respectively.

The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of ${\rm F}_{4(-20)}$