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 SM ISO690:2012ROMANIUC, Simona-Luiza. The Schouten-Van Kampen connection on the tangent bundle endowed with a general natural metric. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 30, 14-17 septembrie 2023, Chişinău. Iași, România: 2023, Ediţia 30, p. 71. |
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| Conference on Applied and Industrial Mathematics Ediţia 30, 2023 |
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Conferința "Conference on Applied and Industrial Mathematics" 30, Chişinău, Moldova, 14-17 septembrie 2023 | ||||||
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| Pag. 71-71 | ||||||
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We determine the Schouten–Van Kampen connection associated to the Levi-Civita connection of a general natural metric on the total space TM of the tangent bundle of a Riemannian manifold. We provide the necessary and sufficient conditions for the obtained Schouten–Van Kampen connection to be torsion free and then to coincide with the Levi-Civita connection. We characterize the general natural α-structures on TM, which are parallel with respect to the torsion free Schouten-Van Kampen connection. Finally, we obtain the (para-)K¨ahler structures of general natural lift type on TM, for which the α-structure is parallel with respect to both Levi-Civita and Schouten-Van Kampen connection. |
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Cerif XML Export
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