Addendum to our paper ``Conformal motion of contact manifolds with characteristic vector field in the \(k\)-nullity distribution''
type: Item
instance of: scholarly article
title: Addendum to our paper ``Conformal motion of contact manifolds with characteristic vector field in the \(k\)-nullity distribution''
zbMATH Open document ID: 0962.53028
published in: Illinois Journal of Mathematics
publication date: 1999-04-22T00:00:00Z
review text: In an earlier paper [\textit{D. E. Blair} and the author, Ill. J. Math. 40, 553-563 (1996; Zbl 0871.53025)], it was proved, as an extension of \textit{M. Okumura}'s result [Tôhoku Math. J., II. Ser. 14, 398-412 (1962; Zbl 0107.16201)] to dimension 3, that, if \(v\) is a non-isometric conformal motion on a 3-dimensional Sasakian manifold \(M\) of constant scalar curvature, then \(M\) is of constant curvature 1 and \(v\) is special concircular. The present paper generalizes the aforementioned result and proves that, if \(v\) is a non-isometric conformal motion on a 3-dimensional Sasakian manifold \(M\) such that \(v\) leaves the scalar curvature of \(M\) invariant, then \(M\) is of constant curvature 1 and \(v\) is special curvature. Hence if, in addition, \(M\) is complete and connected then \(M\) is isometric to a unit sphere.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 1262682
zbMATH Keywords: conformal motion
zbMATH Keywords: 3-dimensional Sasakian manifold
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: sphere
author: Ramesh Sharma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1262682