Kodai Mathematical Journal

On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type

Aydin Gezer and Murat Altunbas

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let (M,g) be an n-dimensional Riemannian manifold and T11(M) be its (1,1)-tensor bundle equipped with the rescaled Sasaki type metric Sgf which rescale the horizontal part by a non-zero differentiable function f. In the present paper, we discuss curvature properties of the Levi-Civita connection and another metric connection of T11(M). We construct almost product Riemannian structures on T11(M) and investigate conditions for these structures to be locally decomposable. Also, some applications concerning with these almost product Riemannian structures on T11(M) are presented. Finally we introduce the rescaled Sasaki type metric Sgf on the (p,q)-tensor bundle and characterize the geodesics on the (p,q)-tensor bundle with respect to the Levi-Civita connection and another metric connection of Sgf.

Article information

Source
Kodai Math. J., Volume 38, Number 1 (2015), 37-64.

Dates
First available in Project Euclid: 18 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1426684442

Digital Object Identifier
doi:10.2996/kmj/1426684442

Mathematical Reviews number (MathSciNet)
MR3323513

Zentralblatt MATH identifier
1326.53038

Citation

Gezer, Aydin; Altunbas, Murat. On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type. Kodai Math. J. 38 (2015), no. 1, 37--64. doi:10.2996/kmj/1426684442. https://projecteuclid.org/euclid.kmj/1426684442


Export citation