Mathematics – Differential Geometry
Scientific paper
2005-03-24
Publ. Math. Debrecen 63/4 (2003), 565 -- 567
Mathematics
Differential Geometry
13 pages
Scientific paper
We consider a unit normal vector field of (local) hyperfoliation on a given Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki metric. We give an explicit expression of the second fundamental form for this submanifold and a rather simple condition its totally geodesic property in the case of a totally umbilic hyperfoliation. A corresponding example shows the non-triviality of this condition. In the 2-dimensional case, we give a complete description of Riemannian manifolds admitting a geodesic unit vector field with totally geodesic property.
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