Contactly geodesic transformations of almost-contact metric structures
type: Item
instance of: scholarly article
title: Contactly geodesic transformations of almost-contact metric structures
zbMATH Open document ID: 1121.53023
author: V. F. Kirichenko
author: N. N. Dondukova
published in: Mathematical Notes
publication date: 2007-05-21T00:00:00Z
review text: For two pseudo-Riemannian manifolds \((M,g)\) and \((\overline M,\overline g)\) a diffeomorphism \(\varphi: M\to\overline M\) is called a geodesic map if \(\varphi\) takes any geodesic in \(M\) to a geodesic in \(\overline M\). \(M\) inherits a new pseudo-Riemannian metric \(\varphi^*\overline g\) which is referred to as a geodesic transformation of the initial metric. Let \(A{\mathcal C}\) be an almost contact structure on a \((2m+1)\)-dimensional pseudo-Riemannian manifold \(M\). A geodesic transformation of the metric of \(A{\mathcal C}\)-structure is said to be contactly geodesic, or briefly \(c\)-geodesic if \(M\) with this transformed metric admits an \(A{\mathcal C}\)-structure. In the case when \(A{\mathcal C}\) is normal in the sense of \textit{V. F. Kirichenko} [Differential-geometric structures on manifolds, Moscow State Pedagogical Univ., Moscow (2003)], it is shown that any \(c\)-geodesic transformation of the metric takes any normal \(A{\mathcal C}\)-structure to a normal \(A{\mathcal C}\)-structure, while a cosymplectic manifold admits no nontrivial \(c\)-geodesic transformation of the metric. The latter statement remains true for Sasakian or Kenmotsu contact manifolds.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53B10
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 5155517
zbMATH Keywords: pseudo-Riemannian manifold
zbMATH Keywords: geodesic transformation
zbMATH Keywords: cosymplectic manifold
zbMATH Keywords: Sasakian manifold
zbMATH Keywords: Kenmotsu manifold
zbMATH Keywords: Riemann-Christoffel tensor
zbMATH Keywords: almost-contact structure
reviewed by: Tanjiro Okubo
MaRDI profile type: Publication
full work available at URL: s11006-006-0129-0
OpenAlex ID: W2020006720
cites work: Q3776971
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cites work: Generalized quasi-Kaehlerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry. II
cites work: Methods of generalized Hermitian geometry in the theory of almost-contact manifolds
cites work: Contact manifolds in Riemannian geometry
cites work: A class of almost contact Riemannian manifolds
DOI: 10.1007/S11006-006-0129-0
description: scientific article; zbMATH DE number 5155517