H. Elhendi, M. Terbeche and D. Mustapha Received: February 24, 2013; Revised: January 28, 2014; Accepted: February 25, 2014 Abstract. The problem studied in this paper is related to the biharmonicity of a section from a Riemannian manifold (M, g) to its tangent bundle of order two T 2M equipped with the diagonal metric gD. We show that a section on a compact manifold is biharmonic if and only if is harmonic. We also investigate the curvature of (T 2M, gD) and the biharmonicity of section of M, as a map from (M, g) to (T 2M, gD). Keywords: Diagonal metric; $\lambda$-lift; biharmonic section. AMS Subject classification: Primary: 30C10, 30C15 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |