On totally geodesic foliations with bundle-like metric |
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Authors: | Aurel Bejancu Hani Reda Farran |
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Institution: | (1) Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait |
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Abstract: | Let
be a totally geodesic foliation of dimension n and codimension p on a Riemannian manifold (M, g). Suppose that g is a bundle-like metric for
and M has at least one point at which none of its mixed sectional curvatures vanishes. Under these conditions we prove that n ≤ p − 1. We show that this inequality is optimal, and none of the above conditions can be removed. |
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Keywords: | 53C12 53C20 |
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