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Keywords:
supermanifolds; curves; jets; higher order tangent bundles
supermanifolds; curves; jets; higher order tangent bundles
Summary:
In this paper we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we make a quick comparison with the notion of a curve presented here are other common notions found in the literature.
References:
[1] Alldridge, A.: A convenient category of supermanifolds. arXiv:1109.3161 [math.DG] 2011.
[2] Cariñena, J.F., Figueroa, H.: Geometric formulation of higher order Lagrangian systems in supermechanics. Acta Appl. Math. 51 (1998), 25–58. DOI 10.1023/A:1005870025318 | MR 1609857 | Zbl 0999.70018
[3] Carmeli, C., Caston, L., Fioresi, R.: Mathematical Foundations of Supersymmetry. EMS Series of Lectures in Mathematics, European Mathematical Society, 2011. MR 2840967 | Zbl 1226.58003
[4] Deligne, P., Morgan, J.W.: Notes on supersymmetry (following Joseph Bernstein). Quantum fields and strings: a course for mathematicians, Amer. Math. Soc., Providence, RI, 1999, Vol. 1, 2 (Princeton, NJ, 1996/1997), pp. 41–97. MR 1701597 | Zbl 1170.58302
[5] DeWitt, B.: Supermanifolds. Cambridge Monogr. Math. Phys., Cambridge University Press, 1984. MR 0778559 | Zbl 0551.53002
[6] di Bruno, F. Faà: Sullo sviluppo delle Funzioni. Annali di Scienze Matematiche e Fisiche 6 (1855), 479–480, (in Italian).
[7] Dumitrescu, F.: Superconnections and parallel transport. Pacific J. Math. 236 (2008), 307–332. DOI 10.2140/pjm.2008.236.307 | MR 2407109 | Zbl 1155.58001
[8] Garnier, S., Wurzbacher, T.: The geodesic flow on a Riemannian supermanifold. J. Geom. Phys. 62 (2012), 1489–1508. DOI 10.1016/j.geomphys.2012.02.002 | MR 2911220 | Zbl 1242.53046
[9] Goertsches, O.: Riemannian supergeometry. Math. Z. 260 (2008), no. 3, 557–593. MR 2434470 | Zbl 1154.58001
[10] Grabowski, J., Rotkiewicz, M.: Graded bundles and homogeneity structures. J. Geom. Phys. 62 (2011), 21–36. DOI 10.1016/j.geomphys.2011.09.004 | MR 2854191
[11] Hélein, F.: An introduction to supermanifolds and supersymmetry. Systèmes intégrables et théorie des champs quantiques (Baird, P., Hélein, F., Kouneiher, J., Pedit, F., Roubtsov, V., eds.), Hermann, 2009, pp. 103–157.
[12] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer–Verlag, 1993, http://www.emis.de/monographs/KSM/index.html MR 1202431
[13] Lane, S. Mac: Categories for the working mathematician. Graduate Texts in Mathematics, vol. 5, Springer–Verlag, New York, 1998, Second Edition. MR 1712872
[14] Manin, Y.: Gauge Field Theory and Complex Geometry. Springer, 1997, Second Edition. MR 1632008 | Zbl 0884.53002
[15] Rogers, A.: A global theory of supermanifolds. J. Math. Phys. 21 (1980), 1352–1365. DOI 10.1063/1.524585 | MR 0574696 | Zbl 0447.58003
[16] Rogers, A.: Supermanifolds: theory and applications. World Scientific, 2007. MR 2320438 | Zbl 1135.58004
[17] Shvarts, A.S.: On the definition of superspace. Teoret. Mat. Fiz. 60 (1984), no. 1, 37–42. MR 0760438 | Zbl 0575.58005
[18] Van Proeyen, A.: Superconformal symmetry and higher-derivative Lagrangians. Breaking of supersymmetry and Ultraviolet Divergences in extended Supergravity, Frascati, 2013, arXiv:1306.2169 [hep-th].
[19] Varadarajan, V.S.: Supersymmetry for Mathematicians: An Introduction. Courant Lecture Notes, vol. 11, Providence, RI: American Mathematical Society, 2004. MR 2069561 | Zbl 1142.58009
[20] Voronov, A.A.: Maps of supermanifolds. Teoret. Mat. Fiz. 60 (1984), no. 1, 43–48, (Russian). MR 0760439
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