INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION

A. Gezer; K. Akbulut

Research Article

INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION

Year 2006, Volume: 35 Issue: 2, 155 - 159, 01.02.2006

Abstract

The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.

Keywords

Lift, Tangent bundle, Infinitesimal affine transformation, Fibre-preserving transformation

References

Yano K. and Ishihara, S. Tangent and cotangent bundles (Marcel Dekker, New York, 1973).
Magden A. and Salimov, A. A. Horizontal lifts of tensor fields to sections of the tangent bundle. (in Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 3, 77–80, 2001.
Kobayashi S. and Nomizu K. Foundations of Differential Geometry (Wiley-Inter Science Publications, New York, 1963).

INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION

Year 2006, Volume: 35 Issue: 2, 155 - 159, 01.02.2006

A. Gezer K. Akbulut

Abstract

References

Yano K. and Ishihara, S. Tangent and cotangent bundles (Marcel Dekker, New York, 1973).
Magden A. and Salimov, A. A. Horizontal lifts of tensor fields to sections of the tangent bundle. (in Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 3, 77–80, 2001.
Kobayashi S. and Nomizu K. Foundations of Differential Geometry (Wiley-Inter Science Publications, New York, 1963).

There are 3 citations in total.

Details

Primary Language	English
Subjects	Statistics
Journal Section	Mathematics
Authors	A. Gezer This is me K. Akbulut This is me
Publication Date	February 1, 2006
Published in Issue	Year 2006 Volume: 35 Issue: 2

Cite

APA	Gezer, A., & Akbulut, K. (2006). INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION. Hacettepe Journal of Mathematics and Statistics, 35(2), 155-159.
AMA	Gezer A, Akbulut K. INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION. Hacettepe Journal of Mathematics and Statistics. February 2006;35(2):155-159.
Chicago	Gezer, A., and K. Akbulut. “INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION”. Hacettepe Journal of Mathematics and Statistics 35, no. 2 (February 2006): 155-59.
EndNote	Gezer A, Akbulut K (February 1, 2006) INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION. Hacettepe Journal of Mathematics and Statistics 35 2 155–159.
IEEE	A. Gezer and K. Akbulut, “INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION”, Hacettepe Journal of Mathematics and Statistics, vol. 35, no. 2, pp. 155–159, 2006.
ISNAD	Gezer, A. - Akbulut, K. “INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION”. Hacettepe Journal of Mathematics and Statistics 35/2 (February 2006), 155-159.
JAMA	Gezer A, Akbulut K. INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION. Hacettepe Journal of Mathematics and Statistics. 2006;35:155–159.
MLA	Gezer, A. and K. Akbulut. “INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION”. Hacettepe Journal of Mathematics and Statistics, vol. 35, no. 2, 2006, pp. 155-9.
Vancouver	Gezer A, Akbulut K. INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION. Hacettepe Journal of Mathematics and Statistics. 2006;35(2):155-9.