Pseudohermitian biminimal Legendre surfaces in the 5-dimensional sphere (Q902241)

The authors study pseudo-Hermitian biminimal Legendre surfaces in a 5-dimensional Sasakian space form of constant sectional curvature for the Tanaka-Webster connection. The main theorem of the paper describes a local structure of such Legendre surfaces. In particular, the authors show that the product of a circle and a helix of order 4 is realized as a nonminimal pseudo-Hermitian biminimal Legendre immersion into \(S^5\). Moreover, such a Legendre surface is mass-symmetric and of 2-type. From the main theorem it follows that there exist no nonminimal pseudo-Hermitian biminimal Legendre surfaces in a 5-dimensional Sasakian space form of non-positive constant holomorphic sectional curvature for the Tanaka-Webster connection.