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Stable harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature

Jintang Li (2010)

Annales Polonici Mathematici

We study the stability of harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature, and we prove that if Mⁿ is a compact Einstein Riemannian minimal submanifold of a Riemannian unit sphere with Ricci curvature satisfying R i c M > n / 2 , then there is no non-degenerate stable harmonic map between M and any compact Finsler manifold.

Subriemannian geodesics of Carnot groups of step 3

Kanghai Tan, Xiaoping Yang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In Carnot groups of step  ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.

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