About a class of metrical N-linear connections on the 2-tangent bundle | Zendy

Gheorghe Atanasiu | Zendy; Monica Purcaru | Zendy

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About a class of metrical N-linear connections on the 2-tangent bundle

Author(s) -

Gheorghe Atanasiu,

Monica Purcaru

Publication year - 2007

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil0701113a

Subject(s) - mathematics , tangent bundle , connection (principal bundle) , metric connection , tangent , curvature , pure mathematics , metric (unit) , nonlinear system , torsion (gastropod) , mathematical analysis , bundle , tangent space , combinatorics , geometry , fundamental theorem of riemannian geometry , ricci curvature , medicine , operations management , physics , surgery , quantum mechanics , economics , materials science , composite material

In the paper herein we treat some problems concerning the met- ric structure on the 2-tangent bundle: T2M: We determine the set of all metric semi-symmetric N-linear connections, in the case when the nonlinear connection N is fixed. We prove that the sets: TN of the transformations of N-linear connection having the same nonlinear con- nections N and ms T N of the transformations of metric semi-symmetric N-linear connections, having the same nonlinear connection N, together with the composition of mappings are groups. We obtain some impor- tant invariants of the group ms T N and we give their properties. We also study the transformation laws of the torsion and curvature d-tensor fields, with respect to the transformations of the groups TN and ms T N.

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