INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION
INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION
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,
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- 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).
- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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