BONNET SURFACES WITH NON-FLAT NORMAL BUNDLE IN THE HYPERBOLIC FOUR-SPACE

Atsushi Fujioka (Japan)

Received June 19, 2008

References:

[1] A. Bobenko and U. Eitner, Bonnet surfaces and Painlevé equations, J. Reine Angew. Math. 499 (1998), 47-79. [2] O. Bonnet, Mémoire sur la théorie des surfaces applicables, J. Éc. Polyt. 42 (1867), 72-92. [3] B. Chen, Geometry of Submanifolds, Pure and Applied Mathematics, No. 22. Marcel Dekker, Inc., New York, 1973. [4] A. Fujioka, Bonnet surfaces in four-dimensional space forms, Internat. J. Math. 15(10) (2004), 981-985. [5] A. Fujioka and J. Inoguchi, Bonnet surfaces with constant curvature, Results Math. 33(3-4) (1998), 288-293. [6] A. Fujioka and J. Inoguchi, Timelike Bonnet surfaces in Lorentzian space forms, Differential Geom. Appl. 18(1) (2003), 103-111. [7] W. C. Graustein, Applicability with preservation of both curvatures, Bull. Amer. Math. Soc. 30 (1924), 19-23.

Keywords and phrases: Bonnet surfaces, mean curvature vector, non-flat normal bundle.