Biharmonic surfaces in pseudo-Euclidean spaces. (English) Zbl 0757.53009

Chen, Bang-Yen; Ishikawa, Susumu

Mem. Fac. Sci., Kyushu Univ., Ser. A 45, No. 2, 323-347 (1991).

A surface immersion is called biharmonic, if it is annihilated by the square of its Laplacian. Minimal surfaces are examples, and in Euclidean 3-space they are the only examples. The authors give other examples and classification results in the pseudo-Euclidean case.

Reviewer: D.Ferus (Berlin)

MSC:

53B25	Local submanifolds
31A30	Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions

Keywords:

Laplacian; minimal surfaces