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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

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.

Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry

J. M. Coron, F. Helein (1989)

Compositio Mathematica

Harmonic map heat flow with free boundary.

Ma Li (1991)

Commentarii mathematici Helvetici

Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces.

Qiaoling Wang (2006)

Publicacions Matemàtiques

In this paper, we prove two Liouville theorems for harmonic maps and apply them to study the topology of manifolds with positive spectrum and stable minimal hypersurfaces in Riemannian manifolds with non-negative bi-Ricci curvature.

Harmonic sections and equivariant harmonic maps.

C.M. Wood (1997)

Manuscripta mathematica

Helical Immersions Into a Unit Sphere.

Kunio Sakamoto (1982)

Mathematische Annalen

Highly Connected Taut Submanifolds.

Gudlaugur Thorbergsson (1983)

Mathematische Annalen

Holomorphicity of Minimal Submanifolds in Complex Space Forms.

Gudlaugur Thorbergsson, Maurice Dajczer (1987)

Mathematische Annalen

Homogeneous submanifolds of the hyperbolic space.

Will, A. (1998)

Rendiconti del Seminario Matematico

Hypersurface geometry and Hamiltonian systems of hydrodynamic type.

Miyaoka, R. (1999)

Lobachevskii Journal of Mathematics

Hypersurfaces with constant $k$ -th mean curvature in a Lorentzian space form

Shichang Shu (2010)

Archivum Mathematicum

In this paper, we study $n (n \geq 3)$ -dimensional complete connected and oriented space-like hypersurfaces $M^{n}$ in an (n+1)-dimensional Lorentzian space form $M_{1}^{n + 1} (c)$ with non-zero constant $k$ -th $(k < n)$ mean curvature and two distinct principal curvatures $λ$ and $μ$ . We give some characterizations of Riemannian product $H^{m} (c_{1}) \times M^{n - m} (c_{2})$ and show that the Riemannian product $H^{m} (c_{1}) \times M^{n - m} (c_{2})$ is the only complete connected and oriented space-like hypersurface in $M_{1}^{n + 1} (c)$ with constant $k$ -th mean curvature and two distinct principal curvatures, if the multiplicities of...

Displaying 1 – 14 of 14

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

Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry

Harmonic map heat flow with free boundary.

Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces.

Harmonic sections and equivariant harmonic maps.

Helical Immersions Into a Unit Sphere.

Highly Connected Taut Submanifolds.

Holomorphicity of Minimal Submanifolds in Complex Space Forms.

Homogeneous submanifolds of the hyperbolic space.

Hypersurface geometry and Hamiltonian systems of hydrodynamic type.

Hypersurfaces with constant $k$ -th mean curvature in a Lorentzian space form

Hypersurfaces with Constant Mean Curvature and Prescribed Area.

Hypersurfaces with constant scalar curvature in a hyperbolic space form.

Hypersurfaces with constant scalar or mean curvature in a unit sphere.

Currently displaying 1 – 14 of 14