Harmonicity of vector fields on four-dimensional generalized symmetric spaces

Giovanni Calvaruso

Displaying similar documents to “Harmonicity of vector fields on four-dimensional generalized symmetric spaces”

$φ (Ric)$ -vector fields in Riemannian spaces

Irena Hinterleitner, Volodymyr A. Kiosak (2008)

Archivum Mathematicum

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In this paper we study vector fields in Riemannian spaces, which satisfy $\nabla ϕ = μ$ , $𝐑𝐢𝐜$ , $μ = const.$ We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and $ϕ (Ric)$ -vector fields cannot exist simultaneously. It was found that Riemannian spaces with $ϕ (Ric)$ -vector fields of constant length have constant scalar curvature. The conditions for the existence of $ϕ (Ric)$ -vector fields in symmetric spaces...

Riemannian manifolds with many Killing vector fields

Ann Stehney, Richard Millman (1980)

Fundamenta Mathematicae

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On harmonic vector fields.

Jerzy J. Konderak (1992)

Publicacions Matemàtiques

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A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics. We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics and on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.

2-Killing vector fields on Riemannian manifolds.

Oprea, Teodor (2008)

Balkan Journal of Geometry and its Applications (BJGA)

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Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces $G_{2}$ and $G_{2} / S O (4)$

László Verhóczki (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The exceptional compact symmetric spaces $G_{2}$ and $G_{2} / S O (4)$ admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.

Some properties of distinguished vector fields on Riemannian.

Ferrara, M. (2003)

APPS. Applied Sciences

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Closed conformal vector fields on pseudo-Riemannian manifolds.

Catalano, D.A. (2006)

International Journal of Mathematics and Mathematical Sciences

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On the energy of unit vector fields with isolated singularities

Fabiano Brito, Paweł Walczak (2000)

Annales Polonici Mathematici

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We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').

Biharmonic Riemannian maps

Bayram Ṣahin (2011)

Annales Polonici Mathematici

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We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo-umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the target manifolds.