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Induced Semi-Sprays and Connections on Submanifolds

In: New Developments in Differential Geometry, Budapest 1996

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  • Marcela Popescu

    (University of Craiova, Department of Mathematics)

Abstract

Some kinds of induced semisprays and corresponding non-linear connections on submanifolds are studied in this paper. Some new definitions, as the vertical tangent bundle of a submanifold, are made. As an application, the semi-spray which corresponds to the Cartan non-linear connection of a Lagrange or a Finsler space induces the same objects on a submanifold. In the paper we give a method to induce a nonlinear connection on a submanifold of a Finsler or a Lagrange manifold, which is different from the known methods. The main advantage of our method is that the case of Finsler splitting is more general than the case of a Lagrange metric.

Suggested Citation

  • Marcela Popescu, 1999. "Induced Semi-Sprays and Connections on Submanifolds," Springer Books, in: J. Szenthe (ed.), New Developments in Differential Geometry, Budapest 1996, pages 317-327, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5276-1_23
    DOI: 10.1007/978-94-011-5276-1_23
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