Restricted Jacobi Fields

Year 2021, , 247 - 265, 29.10.2021

Claudiu Remsing Dennis I. Barrett

https://doi.org/10.36890/iejg.945800

Abstract

We generalize the concept of a Jacobi field to nonholonomic Riemannian geometry, considering both nonholonomic Jacobi fields, and, more generally, restricted Jacobi fields. In the first case, the corresponding Jacobi equation involves the nonholonomic connection and the Schouten curvature tensor. In the second case, the Jacobi equation involves connections and curvature tensors arising in the construction of the Wagner curvature tensor. We also briefly discuss the existence of restricted Jacobi fields.

Keywords

Nonholonomic Riemannian structure, Jacobi field, Schouten curvature tensor, Wagner curvature tensor

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