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论文类型：期刊论文

发表时间：2013-06-15

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE、Scopus

卷号：402

期号：2

页面范围：493-504

ISSN号：0022-247X

关键字：Tangent bundle; Cheeger-Gromoll type metric; General metric; Kahlerian structure; Ricci curvature; Scalar curvature

摘要：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.