Submanifolds and the Sasaki Metric

Details Submanifolds and the Sasaki Metric Submanifolds and the Sasaki Metric

2009-06-05

arxiv.org/abs/0906.1174v1

Mathematics

Differential Geometry

Scientific paper

This is the content of a talk given by the author at the 2009 Lehigh University Geometry/Topology Conference. Using the definition of connection given by Dieudonn\'e, the Sasaki metric on the tangent bundle to a Riemannian manifold is expressed in a natural way. Also, the following property is established. The induced metric on the tangent bundle of an isometrically embedded submanifold is the Sasaki metric if and only if the submanifold is totally geodesic.

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