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Magnetic curves on cotangent bundles endowed with the Riemann extension. (English) Zbl 1495.53058

The paper studies geodesics and magnetic geodesics of the natural Riemannian extension \((T^*M,\overline{g})\) of a manifold \(M\) with a symmetric affine connection \(\nabla\), see [O. Kowalski and M. Sekizawa, Publ. Math. 78, No. 3–4, 709–721 (2011; Zbl 1240.53051)]. The main results determine geodesics and magnetic geodesics which appear as integral curves of vertical and complete lifts to \(T^*M\) of a vector field on \(M\). The study is then extended to symplectic hypersufaces in the cotangent bundle as introduced in [C.-L. Bejan et al., Adv. Appl. Clifford Algebr. 27, No. 3, 2333–2343 (2017; Zbl 1390.53037)].

MSC:

53C22 Geodesics in global differential geometry
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C80 Applications of global differential geometry to the sciences
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References:

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[16] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Dekker, New York, 1973. Cornelia-Livia Bejan, Simona-Luiza Druţă-Romaniuc Department of Mathematics and Informatics “Gheorghe Asachi” Technical University of Iaşi Bd. Carol I, No. 1
[17] Iaşi, Romania E-mail: bejanliv@yahoo.com simonadruta@yahoo.com
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