Resumen de Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

Mohamed Tahar Kadaoui Abbassi, Noura Amri, Cornelia Livia Bejan

• The framework of the paper is the phase universe, described by the total space of the cotangent bundle of a manifold M, which is of interest for both mathematics and theoretical physics. When M carries a symmetric linear connection, then T∗M is endowed with a semi-Riemannian metric, namely the classical Riemann extension, introduced by Patterson and Walker and then by Willmore. We consider here a generalization provided by Sekizawa and Kowalski of this metric, called the natural Riemann extension, which is also a metric of signature (n, n). We give the complete classification of conformal and Killing vector fields with respect to an arbitrary natural Riemann extension. Ricci soliton is a topic that has been increasingly studied lately. Necessary and sufficient conditions for the phase space to become a Ricci soliton (or Einstein) are given at the end.