Submanifolds of generalized Sasakian space forms
type: Item
instance of: scholarly article
title: Submanifolds of generalized Sasakian space forms
zbMATH Open document ID: 1176.53047
author: Pablo Alegre
author: Alfonso Carriazo
published in: Taiwanese Journal of Mathematics
publication date: 2009-09-22T00:00:00Z
review text: Recently the authors and \textit{D. E. Blair} introduced in [Isr. J. Math. 141, 157--183 (2004; Zbl 1064.53026)] the notion of a generalized Sasakian space form. In the present paper the submanifolds of such a space form are studied. It is focused on almost semi-invariant submanifolds, which were initiated by \textit{M. M. Tripathi} and \textit{K. D. Singh} [Demonstr. Math. 29, No. 2, 413--426 (1996; Zbl 0896.53041)], followed by \textit{M. M. Tripathi} and \textit{I. Mihai} [Note Mat. 20(2000--2001), No. 2, 135--164 (2001; Zbl 1097.53037)], and generalize invariant, anti-invariant, and slant submanifolds. Sectional curvatures, Ricci tensor and scalar curvature are also studied. The paper finishes with some results about totally umbilical submanifolds.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 5605700
zbMATH Keywords: generalized Sasakian space form
zbMATH Keywords: almost semi-invariant submanifold
zbMATH Keywords: anti-invariant submanifold
zbMATH Keywords: slant submanifold
reviewed by: Ülo Lumiste
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500405448
OpenAlex ID: W1533366724
DOI: 10.11650/TWJM/1500405448
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description: scientific article; zbMATH DE number 5605700