Submanifolds and the Sasaki Metric

Pedro Solórzano

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arXiv · 0906.1174

Submanifolds and the Sasaki Metric

Pedro Solórzano

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Abstract

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 Dieudonné, 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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BibTeX RIS

Pedro Solórzano. 2009-06-05. Submanifolds and the Sasaki Metric. https://arxiv.org/abs/0906.1174

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