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On the Sasaki metric of the normal bundle of a submanifold in Riemannian space. (Russian) Zbl 0633.53071

If F is a submanifold of a Riemannian manifold M, then the normal bundle \(\pi\) : NF\(\to F\) carries the connection D induced by the Levi-Civita connection on M. D induces the decomposition \(T(NF)=\pi^*TF\oplus \pi^*NF\) which allows to construct - in a canonical way - a Riemannian metric g on NF. g is called the Sasaki metric of NF. The curvature tensor of g is studied here. The authors give necessary and (or) sufficient conditions for the flatness of g and sign conditions for the sectional curvature of (NF,g). The proofs are based on the calculation analogous to that of O. Kowalski [J. Reine Angew. Math. 250, 124-129 (1971; Zbl 0222.53044)].
Reviewer: P.Walczak

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B25 Local submanifolds

Citations:

Zbl 0222.53044
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