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Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps

100%

Sinaei Z.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

This paper is a study of harmonic maps fromRiemannian polyhedra to locally non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different assumptions on the source space. First we prove the analogue of the Schoen-Yau Theorem on a complete pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.

Harmonicity of vector fields on four-dimensional generalized symmetric spaces

100%

Calvaruso G.

Open Mathematics

2012

tom 10

nr 2

411-425

Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Open Mathematics

1 Calvaruso G.

1 Sinaei Z.

1 2014

1 2012

Wyniki wyszukiwania

Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps

Harmonicity of vector fields on four-dimensional generalized symmetric spaces