Abstract
In this paper we classify in a global way the umbilical affine definite surfaces in R4 with respect to the Nomizu-Vrancken affine normalization introduced in [NV]. We prove that an affine complete affine definite surface in R4 is umbilical if and only if it is affine equivalent to the complex paraboloid.
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To Professor Katsumi Nomizu on his 70th birthday
Research partially supported by DGICYT Grant PB91-0731-Co3-02
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Martínez, A., Milán, F. A characterization of the complex paraboloid. Results. Math. 27, 302–307 (1995). https://doi.org/10.1007/BF03322833
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DOI: https://doi.org/10.1007/BF03322833