In the Landau–de Gennes theory of liquid crystals, the propensities for alignments of molecules are represented at each point of the fluid by an element Q of the vector space S0 of 3 × 3 real symmetric traceless matrices, or Q-tensors. According to Longa and Trebin [25], a biaxial nematic system is called soft biaxial if the tensor order parameter Q satisfies the constraint tr(Q) = const. After...

The systematic study of harmonic self-maps on cohomogeneity one manifolds has recently been initiated by P\"uttmann and the second named author in \cite{MR4000241}. In this article we investigate corresponding Jacobi equation describing equivariant stability such self-maps. Besides several general statements concerning their explicitly solve for some cases spheres, special orthogonal groups $\S...

We obtain infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds. They arise, after Euclideanization, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L(p,q,r) in five dimensions have cohomogeneity 2 and U(1) x U(1) x U(1) isometry group. They are topologically S(2) x S(3). Their AdS/CFT duals describe quiver theori...