Bulletin of the Belgian Mathematical Society - Simon Stevin

Certain Conformal-like Infinitesimal Symmetries and the Curvature of a Compact Riemannian Manifold

Miguel Ortega, Francisco J. Palomo, and Alfonso Romero

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Abstract

The notion of orthogonally conformal vector field on a Riemannian manifold is introduced. This class of vector fields properly includes the normalization of nowhere zero conformal ones. It is clarified in several examples. An integral inequality which relates the existence of orthogonally conformal vector fields with properties of the Ricci tensor of a compact Riemannian manifold is proved and some applications are shown.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 2 (2011), 223-229.

Dates
First available in Project Euclid: 7 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1307452072

Digital Object Identifier
doi:10.36045/bbms/1307452072

Mathematical Reviews number (MathSciNet)
MR2847758

Zentralblatt MATH identifier
1223.53030

Subjects
Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 57R25: Vector fields, frame fields

Keywords
Orthogonally conformal vector fields orthogonally Killing vector fields Ricci tensor

Citation

Ortega, Miguel; Palomo, Francisco J.; Romero, Alfonso. Certain Conformal-like Infinitesimal Symmetries and the Curvature of a Compact Riemannian Manifold. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 2, 223--229. doi:10.36045/bbms/1307452072. https://projecteuclid.org/euclid.bbms/1307452072


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