Surfaces in Rⁿ²⁻¹ based on harmonic maps S²→ CPⁿ⁻¹

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We show that many surfaces in ⁿ²⁻¹ can be generated by harmonic maps of S²→ CPⁿ⁻¹. These surfaces are based on the projectors in CPⁿ⁻¹ which describe maps of S²→ CPⁿ⁻¹. In the case when these maps form the Veronese sequence all the surfaces have constant curvature.