Article
Kyungpook Mathematical Journal 2023; 63(1): 79-95
Published online March 31, 2023
Copyright © Kyungpook Mathematical Journal.
Notes on the Second Tangent Bundle over an Anti-biparaKaehlerian Manifold
Nour Elhouda Djaa, Aydin Gezer*
Relizane University, Faculty of Sciences and Technology, Department of Mathematics, 48000, Relizane-Algeria
e-mail : djaanor@hotmail.fr
Ataturk University, Faculty of Science, Department of Mathematics, 25240, Erzurum-Turkey
e-mail : aydingzr@gmail.com
Received: February 15, 2022; Accepted: June 8, 2022
In this note, we define a Berger type deformed Sasaki metric as a natural metric on the second tangent bundle of a manifold by means of a biparacomplex structure. First, we obtain the Levi-Civita connection of this metric. Secondly, we get the curvature tensor, sectional curvature, and scalar curvature. Afterwards, we obtain some formulas characterizing the geodesics with respect to the metric on the second tangent bundle. Finally, we present the harmonicity conditions for some maps.
Keywords: Berger type deformed Sasaki metric, anti-biparaKaehlerian structure, geodesics, second tangent bundle