Some Remarks on Manifolds with Vanishing Bochner Tensor

Volume 2, Issue 4, pp 631--638 http://dx.doi.org/10.22436/jmcs.02.04.07

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Authors

Eileen May G. Cariaga - Institute of Mathematics, College of Science, University of the Philippines, Diliman, Quezon City, Philippines Richard S. Lemence - Institute of Mathematics, College of Science, University of the Philippines, Diliman, Quezon City, Philippines Marian P. Roque - Institute of Mathematics, College of Science, University of the Philippines, Diliman, Quezon City, Philippines

Abstract

In this paper, we present our results on Einsteinian, almost Hermitian manifolds with Bochner tensor B = 0. It shall be shown that under some conditions, these Bochner flat manifolds are complex space forms. Moreover, they are also Kähler manifolds with a constant holomorphic sectional curvature. We also present an identity for the Riemannian curvature of a generalized complex space form.

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Keywords

• Complex space forms
• Kähler manifolds
• Bochner tensor
• generalized complex space forms

MSC

•  53C25
•  53C56

References

• [1] T. Koda, Self-dual and anti-Self-dual Hermitian Surfaces, Kodai Math. J., 10 (1987), 335--342
  • View Article
  • Google Scholar


• [2] T. Koda, K. Sekigawa, Self-Dual Einstein Hermitian Surfaces, Advanced Studies in Pure Mathematics, 22 (1993), 123--131
  • Google Scholar


• [3] R. S. Lemence, On Four-Dimensional Generalized Comples Space Forms, Nihonkai Math. J., 15 (2004), 169--176
  • View Article
  • Google Scholar


• [4] K. Matsuo, Pseudo-Bochner Curvature Tensor on Hermitian Manifolds, Colloquium Mathematicum, 80 (1999), 201--209
  • View Article
  • Google Scholar


• [5] K. Sekigawa, On some 4-dimensional compact almost Hermitian manifolds , J. Ramanujan Math. Soc., 2 (1987), 101--116
  • Google Scholar


• [6] K. Sekigawa, T. Koda, Compact Hermitian Surfaces of Pointwise Constant Holomorphic Sectional Curvature, Glasgow Math. J., 37 (1994), 343--349
  • View Article
  • Google Scholar


• [7] S. Tachibana, On the Bochner Curvature Tensor, Natural Science Report, Ochanomizu University, 18 (1967), 15--19
  • View Article
  • Google Scholar


• [8] S. Tachibana, R. C. Liu, Notes on Kahlerian Metrics with Vanishing Bochner Curvature Tensor, Kodai Math. Sem. Rep., 22 (1970), 313--321
  • View Article
  • Google Scholar


• [9] F. Tricerri, L. Vanhecke, Curvature Tensors on Almost Hermitian Manifolds, Transactions of the American Mathematical Society, 267 (1981), 365--398
  • View Article
  • Google Scholar


• [10] L. Vanhecke, The Bochner curvature tensor on almost Hermitian manifolds, Rend. Sem. Mat. Univ. Politec. Torino, 34 (1975/76), 21--38
  • View Article
  • Google Scholar


• [11] L. Vanhecke, On the Decomposition of curvature tensor fields on almost Hermitian manifolds, Proc. Conf. Differential Geometry (Michigan State University), 1976 (1976), 16--33
  • Google Scholar


• [12] L. Vanhecke, F. Bouten, Constant type for almost Hermitian manifolds, Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, 20 (1976), 415--422
  • View Article
  • Google Scholar