Restricted Jacobi Fields

Authors : Claudiu REMSİNG, Dennis I. BARRETT

Pages : 247-265

Doi:10.36890/iejg.945800

View : 9 | Download : 5

Publication Date : 2021-10-29

Article Type : Research Paper

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