About three important transformations groups

  • Authors:

  • Monica A. P. Purcaru;Mirela Târnoveanu;Laura Ciupală

  • Affiliations:

  • Transilvania University of Braşov, Department of Mathematics, Braşov, Romania;Transilvania University of Braşov, Department of Mathematics, Braşov, Romania;Transilvania University of Braşov, Department of Computer Science, Braşov, Romania

  • Venue:
  • WSEAS Transactions on Mathematics
  • Year:
  • 2010

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Abstract

In the present paper we introduce the concepts of conformal metrical d-structure and of conformal metrical N-linear connection with respect to the conformal metrical d-structure, corresponding to an 1-form on a generalized Hamilton space. We determine the set of all conformal metrical N-linear connections in the case when the nonlinear connection is arbitrary and we find important examples and particular cases. We find the transformations group of these connections. We study the role of the torsion d-tensor fields Tjki Sjki and Sijk in this theory, especially in the determination of the set of all semisymmetric conformal metrical N-linear connections with respect to the conformal metrical d-structure, corresponding to the same nonlinear connection N. We give the transformations group of these connections and other two important groups and we find their remarkable invariants. Finally we determine the set of all metrical N-linear connections in the case when the nonlinear connection is arbitrary, we give important examples and particular cases and for the case when the nonlinear connection is fixed we find the transformations group of these connections.