Old and new structures on the tangent bundle. (English) Zbl 1126.53020

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 264-278 (2007).
The paper under review extends definitions and results on Sasakian and Cheeger-Gromoll metrics. More precisely, the author constructs the metric introduced by M. Anastasiei [Libertas Math. 19, 71–76 (1999; Zbl 0982.53064)], using the general method of Riemannian metrics on the tangent bundle TM given by E. Musso and F. Tricerri [Ann. Mat. Pura Appl. (4) 150, 1–19 (1988; Zbl 0658.53045)]. Furthermore, with the help of a compatible almost complex structure he obtains conditions under which TM is Kählerian, almost Kählerian, or locally conformal Kählerian. The paper ends with conditions when TM is of constant scalar or sectional curvature and with examples of such metrics.
For the entire collection see [Zbl 1108.53003].


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds