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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This note is about the interplay between the almost-hermitian and Riemanniangeometries of a manifold. These geometries can be seen to interact throughcurvature. The main result is an obstruction equation to the integrability ofalmost-complex structures orthogonal with respect to Riemannian metrics withconstrained sectional curvature. Several geometric consequences ensue, such asa formula for the norm of the Levi-Civita covariant derivative of ahypothetical orthogonal complex structure. Our results lead to a partialrecovery of the well-known fact that the round $6$-sphere $S^6$ is nothermitian. The partial proof is intrinsic in nature, and shows some level ofpromise when it comes to generalizing the non-complexity of the round $S^6$result in new directions.

Curvature, integrability, and the six sphere