Monica Purcaru and Marius Paun: A remarkable transformations group on the tangent bundle, p.89-96

Abstract:

In the present paper starting from the notion of metrical structure on the tangent bundle, we determine all metrical d-linear connections in the case when the nonlinear connection is arbitrary and we find important particular cases. We study the role of the torsion tensor fields: T and S in this theory. We find the group of transformations of semi-symmetric metrical d-linear connections, corresponding to the same nonlinear connection N, and its important invariants.

Key Words: Tangent bundle, d-linear connection, curvature, tor-sion, metrical structure, metrical d-linear connection, semi-symmetric metrical d-linear connection, invariants.

2000 Mathematics Subject Classification: Primary: 53C05, Secondary 53C20, 53C60, 53B40, 58B20.

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