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On a superspray in Lagrange superspaces. (English) Zbl 1087.58002

Summary: The notion of Finsler superspace was introduced by S. Vacaru. In this paper we will show that in a Finsler superspace, each Finsler metric induces a superspray. By using this superspray we generate a sequence of nonlinear connections associated to it. In a particular case when we use an affine Berwald-type connection, this sequence is constant.

MSC:

58A50 Supermanifolds and graded manifolds
53C05 Connections (general theory)
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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[1] Bejancu, A., (A New Viewpoint on Differential Geometry of Supermanifolds, I (1990), Timisoara University Press: Timisoara University Press Timisoara, Romania), Ellis Horwood Ltd. · Zbl 0888.58002
[2] Bejancu, A., (A New Viewpoint on Differential Geometry of Supermanifolds, II (1990), Timisoara University Press: Timisoara University Press Timisoara, Romania), Ellis Horwood Ltd. · Zbl 0888.58002
[3] Bartocci, C.; Bruzzo, U.; Hernandez-Ruiperez, D., The Geometry of Supermanifolds (1991), Kluwer Academic Publishers · Zbl 0801.58001
[4] Berwald, L., Untersuchung der Krümmung allgemeiner metrischer Räume auf Grund des in ihnen herrschenden Parallelismus, Math. Z., 25, 40-73 (1926) · JFM 52.0726.04
[5] Cartan, E., Les Espaces de Finsler (1934), Hermann: Hermann Dordrecht · JFM 60.0648.04
[6] Chern, S. S., On the Euclidean connections in Finsler spaces, (Proc. National Acad. Soc., 29 (1943)), 33-37 · Zbl 0060.39210
[7] DeWitt, B., Supermanifolds (1992), Cambridge University Press: Cambridge University Press Paris · Zbl 0874.53055
[8] Esrafilian, E.; Azizpour, E., Nonlinear connections and supersprays in supermanifolds, Rep. Math. Phys., 54, 365-372 (2004) · Zbl 1066.58004
[9] Jadczyk, A.; Pilch, K., Superspaces and supersymmetries, Commun. Math. Phys., 78, 373-390 (1980) · Zbl 0464.58006
[10] Kawaguchi, A., Beziehung zwischen einer metrischen linearen Übertrangung and einer nichtmetrischen in einem allgemeinen metrischen Räume, (Proc. Akad. Wet. Amsterdam, 40 (1937)), 596-601 · JFM 63.0698.01
[11] Kawaguchi, A., On the theory of non-linear connections II.Theory of Minkowski spaces and of non-linear connections in Finsler spaces, Tensor, New Ser., 6, 165-199 (1956) · Zbl 0073.39002
[12] Ehresmann, C., Les connexions infinitésimales dans un espace fibré différentiable, Coll. Topologia, Bruxelles, 29-55 (1955)
[13] Barthel, W., Nichtlineare Zusammenhänge und deren Holonomie Gruppen, J. Reine Angew. Math., 212, 120-149 (1963) · Zbl 0115.39704
[14] Leites, D., Introduction to the Theory of Supermanifolds, Russian. Math. Surveys., 35, 1-64 (1980) · Zbl 0462.58002
[15] Miron, R.; Anastasiei, M., The Geometry of Lagrange Spaces: Theory and Applications (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Cambridge · Zbl 0831.53001
[16] Shen, Z., Differential Geometry of Sprays and Finsler Spaces (2001), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht
[17] Vacaru, S. I., Superstrings in higher order extensions of Finsler superspaces, Nucl. Phys., B494, no. 3, 590-656 (1997) · Zbl 0934.81032
[18] Vacaru, S. I., Nonlinear Connections in Superbundles and Locally Anisotropic Supergravity, E-print
[19] Vacaru, S. I., Interactions, Strings and Isotopies in Higher Order Anisotropic Superspaces (1998), Hadronic Press: Hadronic Press Dordrecht · Zbl 0954.53049
[20] Vacaru, S. I., Generalized Finsler Geometry in Einstein, String and Metric-Affine Gravity, E-print · Zbl 0972.83047
[21] Vacaru, S. I., Nonholonomic Clifford Structures and Noncommutative Riemann-Finsler Geometry, E-print · Zbl 0972.83047
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