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Zbl 1126.53020
Munteanu, Marian Ioan
Old and new structures on the tangent bundle. (English)
[A] Mladenov, Iva\"ilo (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. 264-278 (2007). ISBN 978-954-8495-37-0/pbk

The paper under review extends definitions and results on Sasakian and Cheeger-Gromoll metrics. More precisely, the author constructs the metric introduced by {\it 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 {\it E. Musso} and {\it 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.
[Demetra Demetropoulou-Psomopoulou (Thessaloniki)]

MSC 2000:: *53C15 Geometric structures on manifolds
53C25 Special Riemannian manifolds
53C55 Complex differential geometry (global)

Keywords: compatible almost complex structure; constant sectional curvature curvature; constant scalar curvature

Citations: Zbl 0982.53064; Zbl 0658.53045

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