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.
Nonholonomic Riemannian structure Jacobi field Schouten curvature tensor Wagner curvature tensor
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 29 Ekim 2021 |
Kabul Tarihi | 25 Temmuz 2021 |
Yayımlandığı Sayı | Yıl 2021 |