Displaying similar documents to “Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps”

Some examples of harmonic maps for g -natural metrics

Mohamed Tahar Kadaoui Abbassi, Giovanni Calvaruso, Domenico Perrone (2009)

Annales mathématiques Blaise Pascal

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We produce new examples of harmonic maps, having as source manifold a space ( M , g ) of constant curvature and as target manifold its tangent bundle T M , equipped with a suitable Riemannian g -natural metric. In particular, we determine a family of Riemannian g -natural metrics G on T 𝕊 2 , with respect to which all conformal gradient vector fields define harmonic maps from 𝕊 2 into ( T 𝕊 2 , G ) .

Metric Perspectives of the Ricci Flow Applied to Disjoint Unions

Sajjad Lakzian, Michael Munn (2014)

Analysis and Geometry in Metric Spaces

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In this paper we consider compact, Riemannian manifolds M1, M2 each equipped with a oneparameter family of metrics g1(t), g2(t) satisfying the Ricci flow equation. Adopting the characterization of super-solutions to the Ricci flow developed by McCann-Topping, we define a super Ricci flow for a family of distance metrics defined on the disjoint union M1 ⊔ M2. In particular, we show such a super Ricci flow property holds provided the distance function between points in M1 and M2 is itself...

On almost-Riemannian surfaces

Roberta Ghezzi (2010-2011)

Séminaire de théorie spectrale et géométrie

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An almost-Riemannian structure on a surface is a generalized Riemannian structure whose local orthonormal frames are given by Lie bracket generating pairs of vector fields that can become collinear. The distribution generated locally by orthonormal frames has maximal rank at almost every point of the surface, but in general it has rank 1 on a nonempty set which is generically a smooth curve. In this paper we provide a short introduction to 2-dimensional almost-Riemannian geometry highlighting...

From infinitesimal harmonic transformations to Ricci solitons

Sergey E. Stepanov, Irina I. Tsyganok, Josef Mikeš (2013)

Mathematica Bohemica

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The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.