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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Restricted Jacobi Fields

Dennis I. Barrett and Claudiu C. Remsing
Pages
247–265
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also briefly discuss the existence of restricted Jacobi fields.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We generalize the concept of a Jacobi field to nonholonomic Riemannian geometry, considering both nonholonomic Jacobi fields, and, more generally, restricted Jacobi fields.
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Key Findings & Data:In the first case, the corresponding Jacobi equation involves the nonholonomic connection and the Schouten curvature tensor.
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Conclusion & Impact:We also briefly discuss the existence of restricted Jacobi fields.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Nonholonomic Riemannian structure · Jacobi field · Schouten curvature tensor

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.

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Cite This Article

Remsing, D. I. B. A. C. C. (2022). Restricted Jacobi Fields. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 247–265. https://ajindex.com/articles/539596

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