ON THE LIFTS OF SEMI-RIEMANNIAN METRICS
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-Rie...
Saved in:
| Format: | Article |
|---|---|
| Language: | English |
| Published: |
University of Tehran
1994-12-01
|
| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31195_4e3b50f3c704f94c257725bd4f808c71.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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 |
|---|---|
| ISSN: | 1016-1104 2345-6914 |