Abstract
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.
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Acknowledgements
The authors would like to express their sincere gratitude to Professor M. Sekizawa for helpful comments and suggestions, and to the unknown referee for his/her careful reading of the manuscript.
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Dedicated to the memory of Professor Vasile Oproiu (1941–2020).
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Abbassi, M.T.K., Amri, N. & Bejan, CL. Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions. Mediterr. J. Math. 18, 55 (2021). https://doi.org/10.1007/s00009-020-01690-5
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DOI: https://doi.org/10.1007/s00009-020-01690-5