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

We prove that the horizontal and vertical distributions of the tangent bundlewith the Sasaki metric are isocline, the distributions given by the kernels ofthe horizontal and vertical lifts of the contact form $\omega$ from theHeisenberg manifold $(H_3,g)$ to $(TH_3,g^S)$ are not totally geodesic, and thedistributions $F^H=L(E_1^H,E_2^H)$ and $F^V=L(E_1^V,E_2^V)$ are totallygeodesic, but they are not isocline. We obtain that the horizontal and naturallifts of the curves from the Heisenberg manifold $(H_3,g)$, are geodesics inthe tangent bundle endowed with the Sasaki metric $(TH_3,g^s)$, if and only ifthe curves considered on the base manifold are geodesics. Then, we get twoparticular examples of geodesics from $(TH_3,g^s)$, which are not horizontal ornatural lifts of geodesics from the base manifold $(H_3,g)$.

Geodesicity and Isoclinity Properties for the Tangent Bundle of the Heisenberg Manifold with Sasaki Metric