The main purpose of this paper is to investigate some relations between the flatness or locally symmetric property on the tangent bundle TM equipped with the metric II+III and the same property on the base manifold M and study geodesics by means of the adapted frame on TM.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-6, author = {A. Gezer and O. Tarakci and A. A. Salimov}, title = {On the geometry of tangent bundles with the metric II+III}, journal = {Annales Polonici Mathematici}, volume = {98}, year = {2010}, pages = {73-85}, zbl = {1186.53057}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-6} }
A. Gezer; O. Tarakci; A. A. Salimov. On the geometry of tangent bundles with the metric II+III. Annales Polonici Mathematici, Tome 98 (2010) pp. 73-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-6/