Geometric properties of some classes of Riemannian almost-product manifolds
type: Item
instance of: scholarly article
title: Geometric properties of some classes of Riemannian almost-product manifolds
zbMATH Open document ID: 0538.53043
DOI: 10.1007/BF02848536
author: O. Gil-Medrano
publication date: 1983-01-01T00:00:00Z
review text: In a recent paper, the reviewer has defined 36 different classes of Riemannian almost-product manifolds by the properties of the tensor field \(\nabla P\), \(P\) being the almost-product structure, \(\nabla\) the Levi-Civita connection [Rend. Mat. Appl., VII. Ser. 3, 577--592 (1983; Zbl 0538.53045) (see the second review below)]. In this paper the author defines four algebraic conditions for a distribution on a Riemannian manifold which are sufficient to describe the 36 classes, so simplifying the study of the geometric properties of the classes notably. In particular, the interpretation of many of the classes is given here by finding the geometric meaning of the four properties. The behaviour of the different classes under conformal transformations of the metric is studied by determining how the four conditions are transformed when the metric is conformally changed.
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 3855925
zbMATH Keywords: almost-product manifolds
zbMATH Keywords: almost-product structure
zbMATH Keywords: distribution
zbMATH Keywords: conformal transformations
Wikidata QID: Q115391441
reviewed by: A. M. Naveira
MaRDI profile type: Publication
cites work: Linear invariants of Riemannian almost product manifolds
cites work: Q3700420
cites work: On certain classes of almost product structures
cites work: Q3324604
cites work: The second fundamental form of a plane field
cites work: Q3894668
cites work: Special connections and almost foliated metrics
cites work: A note on complementary subspaces in a Riemannian space
full work available at URL: https://doi.org/10.1007/bf02848536
OpenAlex ID: W1972133993
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 3855925