ON THE LIFTS OF SEMI-RIEMANNIAN METRICS

	ON THE LIFTS OF SEMI-RIEMANNIAN METRICS
Journal of Sciences, Islamic Republic of Iran
مقاله 9، دوره 5، شماره 3، اسفند 1994 اصل مقاله (533.05 K)
چکیده
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

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