Abstract
We classify the magnetic Jacobi fields in cosymplectic manifolds of dimension 3, enriching the results in the study of magnetic Jacobi fields derived from uniform magnetic fields. In particular, we give examples of Jacobi magnetic fields in the Euclidean space E3 and we conclude with the description of magnetic Jacobi fields in the product spaces S2×R and H2×R.
Highlights
It is worth mentioning that a challenging problem was the study of magnetic Jacobi fields in Sasakian manifolds ( M, φ, ξ, η, g)
The complete classification of magnetic Jacobi fields along contact magnetic curves in three-dimensional Sasakian space forms is given in [9], along with explicit examples of magnetic Jacobi fields on the unit 3-sphere S3, on the Heisenberg group Nil3, and on the model space of the SL-geometry SL2 R
Due to the strong connection of our study with the Euclidean 3-space, and since E3 can be endowed with a cosymplectic structure, we gradually introduce the reader in the study of magnetic Jacobi fields, presenting in Section 3 the results obtained in E3
Summary
It is worth mentioning that a challenging problem was the study of magnetic Jacobi fields in Sasakian manifolds ( M, φ, ξ, η, g) In this case the Lorentz force is naturally obtained from the contact magnetic field F = −qdη, q ∈ R, and φ = qφ. The complete classification of magnetic Jacobi fields along contact magnetic curves in three-dimensional Sasakian space forms is given in [9], along with explicit examples of magnetic Jacobi fields on the unit 3-sphere S3 , on the Heisenberg group Nil , and on the model space of the SL-geometry SL2 R These results were developed further for magnetic.
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