Simona-Luiza Druta | Searcharxiv

arXiv2010

Other Classes of Tangent Bundles with General Natural Almost Anti-Hermitian Structures

We continue the study of the anti-Hermitian structures of general natural lift type on the tangent bundles. We get the conditions under which these structures are in the eight classes obtained by Ganchev and Borisov. We complete the characterization of the general natural anti-Kahlerian structures on the tangent bundles with necessary and sufficient conditions, then we present some results concerning the remaining classes.

math.DG↗

arXiv2010

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

We prove that the horizontal and vertical distributions of the tangent bundle with the Sasaki metric are isocline, the distributions given by the kernels of the horizontal and vertical lifts of the contact form $ω$ from the Heisenberg manifold $(H_3,g)$ to $(TH_3,g^S)$ are not totally geodesic, and the distributions $F^H=L(E_1^H,E_2^H)$ and $F^V=L(E_1^V,E_2^V)$ are totally geodesic, but they are not isocline. We obtain that the horizontal and natural lifts of the curves from the Heisenberg manifold $(H_3,g)$, are geodesics in the tangent bundle endowed with the Sasaki metric $(TH_3,g^s)$, if and only if the curves considered on the base manifold are geodesics. Then, we get two particular examples of geodesics from $(TH_3,g^s)$, which are not horizontal or natural lifts of geodesics from the base manifold $(H_3,g)$.

math.DG↗