Optimal inequalities for the normalized \(\delta\)-Casorati curvatures of submanifolds in Kenmotsu space forms
type: Item
instance of: scholarly article
title: Optimal inequalities for the normalized \(\delta\)-Casorati curvatures of submanifolds in Kenmotsu space forms
zbMATH Open document ID: 1430.53065
author: Chul Woo Lee
author: Jae Won Lee
author: Gabriel Eduard Vilcu
publication date: 2018-03-29T00:00:00Z
review text: An almost contact manifold \(\bar{M}\) is said to be \textit{Kenmotsu} whenever the structure tensors \((\phi, \xi, \eta)\) satify certain natural equations involving the Levi-Civita connection \(\bar\nabla\) of the Riemannian metric \(\bar{g}\) of \(\bar{M}\); such an \(\bar{M}\) is a \textit{Kenmotsu space form} whenever its sectional curvatures are the same along all \(\phi\)-holomorphic planes. \textit{Casorati curvatures} of submanifolds of Riemannian spaces are certain scalar quantities expressed in terms of their second fundamental forms. Here, the authors provide certain upper estimates of Casorati curvatures for submanifolds \(M\) of Kenmotsu space forms \(\bar{M}\) provided that \(\dim M = m+1\), \(\dim\bar{M} = 2m+1\) and \(\xi\in TM\).
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D15
zbMATH DE Number: 6854802
zbMATH Keywords: submanifold
zbMATH Keywords: Casorati curvature
zbMATH Keywords: almost contact manifold, Kenmotsu space form
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: advgeom-2017-0008
OpenAlex ID: W2626293890
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DOI: 10.1515/ADVGEOM-2017-0008
published in: advg
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description: scientific article; zbMATH DE number 6854802