On Affine Connections Induced on the (1,1)-Tensor Bundle


ALTUNBAŞ M., GEZER A.

CHINESE ANNALS OF MATHEMATICS SERIES B, vol.39, no.4, pp.683-694, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s11401-018-0089-1
  • Journal Name: CHINESE ANNALS OF MATHEMATICS SERIES B
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.683-694
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T-1(1)(M) its (1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T-1(1)(M) called the intermediate lift connection, which lies somewhere between the complete lift connection and horizontal lift connection. Properties of this intermediate lift connection are studied. Finally, they consider an affine connection induced from this intermediate lift connection on a cross-section sigma(xi)(M) of T-1(1)(M) defined by a (1, 1)-tensor field xi and present some of its properties.