TY - JOUR ID - 31195 TI - ON THE LIFTS OF SEMI-RIEMANNIAN METRICS JO - Journal of Sciences, Islamic Republic of Iran JA - JSCIENCES LA - en SN - 1016-1104 Y1 - 1994 PY - 1994 VL - 5 IS - 3 SP - EP - DO - N2 - In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a manifold, into a semi-Riemannian manifold. When the metric of the vector bundle E is parallel with respect to the chosen connection, we compute the Levi-Civita connection of E, its geodesics, and its curvature tensors. We also show that the sphere and pseudo-sphere bundles of E are nondegenerate submanifolds of E, and we shall compute their second fundamental forms. We shall also prove some results on the metric of E UR - https://jsciences.ut.ac.ir/article_31195.html L1 - https://jsciences.ut.ac.ir/article_31195_4e3b50f3c704f94c257725bd4f808c71.pdf ER -