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Indexed by:期刊论文

Date of Publication:2013-06-15

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、Scopus

Volume:402

Issue:2

Page Number:493-504

ISSN No.:0022-247X

Key Words:Tangent bundle; Cheeger-Gromoll type metric; General metric; Kahlerian structure; Ricci curvature; Scalar curvature

Abstract:In this paper we study the structure of tangent bundle TM of a Riemannian manifold (M, g) with a general metric G(a,b). We prove that (TM, G(a,b)) is flat if and only if it is Kahlerian, and (TM, G(a,b)) is Kahlerian if and only if it is almost Kahlerian and M is flat. We also prove that (TM, G(a,b)) Einstein if and only if both (TM, G(a,b)) and (M, g) are flat. Finally, for M to be a space form with constant curvature, we obtain a necessary and sufficient condition for (TM, G(a,b)) having the constant scalar curvature. (C) 2013 Elsevier Inc. All rights reserved.