Abstract The main result of this paper is an expression the flag curvature a submanifold Randers–Minkowski space $$({\mathscr {V}},F)$$ ( V , F ) in terms invariants related to its Zermelo data ( h , W ). More precisely...

For any G $G$ -invariant metric on a compact homogeneous space M = / K $M=G/K$ , we give formula for the Lichnerowicz Laplacian restricted to of all symmetric 2-tensors in terms structural constants $G/K$ . As an application, compute spectrum Einstein metrics most generalized Wallach spaces and flag manifold with b 2 ( ) 1 $b_2(M)=1$ This allows deduce -stability critical point types each such ...

In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is differentiable and satisfies the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove that the sequence generated by our me...

Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the ‘Bestvina-Brady group’, or ‘Artin kernel’, ΓK . We show that ΓK has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i...