The class of second order equations which Riemannian geometry can be applied to
type: Item
instance of: scholarly article
title: The class of second order equations which Riemannian geometry can be applied to
zbMATH Open document ID: 0797.58009
author: Nobuhiro Innami
published in: Journal of the Mathematical Society of Japan
publication date: 1994-10-11T00:00:00Z
review text: Let \(M\) be a \(C^ \infty\) manifold without boundary and \(TM\) the tangent bundle of \(M\). A second order differential system on \(M\) is considered to be a vector field \(V\) on \(TM\). Let \(f^ t\) be the flow on \(TM\) generated by \(V\). In this note is studied the case that \(f^ t\) has an invariant hypersurface \(S\) in \(TM\) such that all fibres \(S_ x\) are star-shaped hypersurfaces around the origin in \(T_ x M\), \(x \in M\). Using the flows whose trajectories are geodesics and certain positive continuous functions, the author obtains several nontrivial conditions equivalent to the existence of a complementary \(f^ t\)-invariant distribution.
Mathematics Subject Classification ID: 58A30
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 469053
zbMATH Keywords: flows
zbMATH Keywords: geodesics
zbMATH Keywords: distributions
zbMATH Keywords: Riemannian metric
zbMATH Keywords: connection map
reviewed by: Costache Apreutesei
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04510089
OpenAlex ID: W1978935753
Wikidata QID: Q115225522
DOI: 10.2969/JMSJ/04510089
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description: scientific article; zbMATH DE number 469053