Centroaffine First Order Invariants of Surfaces in IR4 |
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Authors: | Christine Scharlach |
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Affiliation: | 1. Fachbereich Mathematik, MA 8-3, Technische Universit?t Berlin, Stra?e des 17. Juni 136, D-10623, Berlin, Germany
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Abstract: | An investigation of the centroaffine geometry of surfaces in IR4 leads to the centroaffine first order invariants: the vector bundle valued second fundamental form, the affine semiconformal structure, the h3-semiconformal structure and the centroaffine metric. A classification of surfaces by their semiconformal structures according to signature and rank is given. This involves the study of the orbits of two pencils of symmetric bilinear forms on IR2 under a change of basis. Combined with previous results ([Nomizu-Sasaki 93]) a complete classification of the zero-degenerate surfaces is obtained and examples of the other surface types are constructed. |
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