Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 165-179
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H. Elhendi; M. Terbeche; Mustapha Djaa; H. Elhendi; M. Terbeche; Mustapha Djaa. Tangent Bundle of Order Two and Biharmonicity. Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 165-179. http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a1/
@article{AMUC_2014_83_2_a1,
author = {H. Elhendi and M. Terbeche and Mustapha Djaa and H. Elhendi and M. Terbeche and Mustapha Djaa},
title = { Tangent {Bundle} of {Order} {Two} and {Biharmonicity}},
journal = {Acta mathematica Universitatis Comenianae},
pages = {165--179},
year = {2014},
volume = {83},
number = {2},
url = {http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a1/}
}
TY - JOUR
AU - H. Elhendi
AU - M. Terbeche
AU - Mustapha Djaa
AU - H. Elhendi
AU - M. Terbeche
AU - Mustapha Djaa
TI - Tangent Bundle of Order Two and Biharmonicity
JO - Acta mathematica Universitatis Comenianae
PY - 2014
SP - 165
EP - 179
VL - 83
IS - 2
UR - http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a1/
ID - AMUC_2014_83_2_a1
ER -
%0 Journal Article
%A H. Elhendi
%A M. Terbeche
%A Mustapha Djaa
%A H. Elhendi
%A M. Terbeche
%A Mustapha Djaa
%T Tangent Bundle of Order Two and Biharmonicity
%J Acta mathematica Universitatis Comenianae
%D 2014
%P 165-179
%V 83
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a1/
%F AMUC_2014_83_2_a1
The problem studied in this paper is related to the biharmonicity of a section from a Riemannian manifold $(M,g)$ to its tangent bundle $T^{2}M$ of order two equipped with the diagonal metric $g^{D}$. We show that a section on a compact manifold is biharmonic if and only if it is harmonic. We also investigate the curvature of $(T^{2}M, g^{D})$ and the biharmonicity of section of $M$ as a map from $(M,g)$ to $(T^{2}M, g^{D})$.
