ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Tangent Bundle of Order Two and Biharmonicity

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