Geodesic
On Weil bundles
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 3, Tome 222 (2023), pp. 100-114.

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In the paper, some lifts of tensor fields and linear connections given on a smooth manifold of the class $C^{\infty}$ to its Weil bundle $M_n^{\mathbb{A}}$ are considered. A brief review of results on the theory of second-order Weil bundles obtained in recent years is given.
Keywords: differentiable manifold, Weil bundle, vertical lift of a tensor field, horizontal lift of a tensor field, horizontal lift of a linear connection, complete lift of a linear connection. 
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A. Ya. Sultanov; O. A. Monakhova; G. A. Sultanova. On Weil bundles. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 3, Tome 222 (2023), pp. 100-114. http://geodesic.mathdoc.fr/item/INTO_2023_222_a9/

[1] Budanov K. M., “Lifty funktsii i vektornykh polei v rassloenie Veilya nad algebroi vysoty”, Differ. geom. mnogoobr. figur., 2006, no. 37, 12–16

[2] Budanov K. M., “Lifty lineinoi svyaznosti i funktsii v rassloenie Veilya nad spetsialnoi algebroi Veilya”, Differ. geom. mnogoobr. figur., 2007, no. 38, 12–16

[3] Budanov K. M., “O liftakh tenzornykh polei tipa $(1,1)$ v rassloenie Veilya nad spetsialnoi algebroi Veilya”, Izv. Penzensk. gos. ped. un-ta. Fiz.-mat. i tekhn. nauki., 2012, no. 30, 28–32

[4] Budanov K. M., Sultanov A. Ya., “Infinitezimalnye affinnye preobrazovaniya rassloeniya Veilya vtorogo poryadka so svyaznostyu polnogo lifta”, Izv. vuzov. Mat., 2015, no. 12, 3–13

[5] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, Izd-vo Kazan. un-ta, Kazan, 1985

[6] Kertis I., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969

[7] Manina N. I., “Nekotorye svoistva gorizontalnogo lifta lineinoi svyaznosti v kasatelnoe rassloenie vtorogo poryadka”, Mat. Vseros. nauch.-prakt. konf. «Fundamentalnye nauki i obrazovanie», BPGU, Biisk, 2006, 39–44

[8] Manina N. I., “Infinitezimalnye affinnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu gorizontalnogo lifta nad neproektivno-ploskim prostranstvom”, Mat. VII Mezhdunar. simp. «Fundamentalnye i prikladnye problemy nauki». T. 1, M., 2012, 23–31

[9] Manina N. I., Sultanov A. Ya., “Infinitezimalnye affinnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu gorizontalnogo lifta”, Izv. vuzov. Mat., 2011, no. 9, 62–69

[10] Osminina N. A., “Ob algebre infinitezimalnykh affinnykh preobrazovanii kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu polnogo lifta”, Dvizheniya v obobschennykh prostranstvakh: Mezhvuz. sb. nauch. tr, PGPU, Penza, 1999, 102–106

[11] Sekacheva N. A., “O kanonicheskom razlozhenii proizvolnogo infinitezimalnogo preobrazovaniya v kasatelnom rassloenii vtorogo poryadka”, Matematika i informatika: Mezhvuz. sb. nauch. tr, PGPU, Penza, 1996, 24–26

[12] Shurygin V. V., “Mnogoobraziya nad algebrami i ikh primenenie v geometrii rassloenii strui”, Usp. mat. nauk., 48:2 (290) (1993), 75–106

[13] Morimoto A., “Liftings of some types of tensor fields and connections to tangent bundles of $p^{v}$-velocities”, Nagoya Math. J., 40 (1970), 13–31 | DOI

[14] Yano K., Tangent and Cotangent Bundles. Differential Geometry, Marcel Dekker, New York, 1973