On invariant submanifolds of \(\mathcal C\)- and \(\mathcal S\)-manifolds
type: Item
instance of: scholarly article
title: On invariant submanifolds of \(\mathcal C\)- and \(\mathcal S\)-manifolds
zbMATH Open document ID: 0992.53018
DOI: 10.1023/A:1006675731141
published in: Acta Mathematica Hungarica
publication date: 2000-05-14T00:00:00Z
review text: \(\mathcal S\)- and \(\mathcal C\)-structures are interesting cases of \(f\)-structures [see \textit{D. E. Blair}, J. Differ. Geom. 4, 155-167 (1970; Zbl 0202.20903)]. First the properties of the second fundamental form and the Weingarten operator are studied, and some observations on the curvature tensors are given. Then it is proved that the second fundamental form of a submanifold of an \(\mathcal S\)-manifold is parallel if and only if it is totally geodesic. By a counterexample it is shown that this is not true for \(\mathcal C\)-manifolds.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 1446810
zbMATH Keywords: totally geodesic invariant submanifold
zbMATH Keywords: \(f\)-structure
zbMATH Keywords: \(\mathcal S\)-manifold
zbMATH Keywords: \(\mathcal C\)-manifold
author: Luigia Di Terlizzi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1446810