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Mediterranean Journal of Mathematics

, Volume 13, Issue 6, pp 3797–3815 | Cite as

Generalized Sasakian Space Forms and Riemannian Manifolds of Quasi Constant Sectional Curvature

  • Avik De
  • Tee-How Loo
Article

Abstract

In this paper, we show that a generalized Sasakian space form of dimension >3 is either of constant sectional curvature, or a canal hypersurface in Euclidean or Minkowski spaces, or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold, or locally a warped product of a real line and a generalized complex space form, or an \({\alpha}\)-Sasakian space form, or it is of five dimension and admits an \({\alpha}\)-Sasakian Einstein structure. In particular, a local classification for generalized Sasakian space forms of dimension >5 is obtained. A local classification of Riemannian manifolds of quasi constant sectional curvature of dimension >3 is also given in this paper.

Keywords

Generalized Sasakian space forms generalized complex space forms canal hypersurfaces Riemannian manifolds of quasi constant sectional curvature trans-Sasakian manifolds 

Mathematics Subject Classification

Primary 53C25 53C15 Secondary 53B20 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematical and Actuarial SciencesUniversiti Tunku Abdul RahmanCherasMalaysia
  2. 2.Institute of Mathematical SciencesUniversity of MalayaKuala LumpurMalaysia

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