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arXiv · 1508.00302

Generalized Sasakian space forms and Riemannian manifolds of quasi constant sectional curvature

Avik De·Tee-How Loo
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Abstract

In this paper, we show that a generalized Sasakian space form of dimension greater than three 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 wapred product of a real line and a generalized complex space form; or an $α$-Sasakian space form; or it is of five dimension and admits an $α$-Sasakian Einstein structure. In particular, a local classification for generalized Sasakian space forms of dimension greater than five is obtained. A local classification of Riemannian manifolds of quasi constant sectional curvature of dimension greater than three is also given in this paper.

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Avik De, Tee-How Loo. 2015-08-03. Generalized Sasakian space forms and Riemannian manifolds of quasi constant sectional curvature. https://arxiv.org/abs/1508.00302

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