We introduce a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds. We then apply this for the important semisimple Lie groups SO(n), SU(n), Sp(n), SL n (R), Sp(n, R), SU(p, q), SO(p, q), Sp(p, q), SO * (2n) and SU * (2n). Keywords Biharmonic functions • p-harmonic functions • Semisimple Lie groups Mathematics Subject Classification 31B30 • 53C43 • 58E20 2 Preliminaries Let (M, g) be a smooth manifold equipped with a Riemannian metric g. We complexify the tangent bundle T M of M to T C M and extend the metric g to a complex-bilinear form on B Sigmundur Gudmundsson

In this work we construct explicit complex-valued p-harmonic functions on the compact Riemannian symmetric spaces SU(n)/SO(n), Sp(n)/U(n), SO(2n)/U(n), SU(2n)/Sp(n). We also describe how the same can be manufactured on their non-compact symmetric dual spaces.

In this work we construct explicit complex-valued p-harmonic functions on the compact Riemannian symmetric spaces $$\mathbf{SU} (n)/\mathbf{SO} (n)$$ SU ( n ) / SO ( n ) , $$\mathbf{Sp} (n)/\mathbf{U} (n)$$ Sp ( n ) / U ( n ) , $$\mathbf{SO} (2n)/\mathbf{U} (n)$$ SO ( 2 n ) / U ( n ) , $$\mathbf{SU} (2n)/\mathbf{Sp} (n)$$ SU ( 2 n ) / Sp ( n ) . We also describe how the same can be manufactured on their non-compact symmetric dual spaces.

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We introduce a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds. We then apply this for the important semisimple Lie groups SO(n), SU(n), Sp(n), SLn(R), Sp(n, R), SU(p, q), SO(p, q), Sp(p, q), SO * (2n) and SU * (2n).