Totally Geodesic Submanifolds of a Linearly Connected Manifold without Torsion
✍ Scribed by Dečko Mitov
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 744 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
It is well-known that the geodesics of a linearly connected manifold ilrJ are obtained by projection of the integral curvea of the standard horizontal vector fields onto 144. We study special distributions on the bundle of linear frames of V when the linear connection has no torsion. The projections of their integral manifolds onto 21 are totally geodesic submanifolds of M and, conversely, every totally geodesic submanifold can be obtained in this way. The last section of the paper contains a treatment of linear connections with recurrent curvature. In particular. some propositions about the rank of a manifold with recurrent curvature are proved.