We study isoparametric hypersurfaces, whose principal curvatures are all constant, in the pseudo-Riemannian space forms. In this paper, we investigate three topics. Firstly, according to Petrov's classification theorem, we give a classification of hypersurfaces of index 2 with respect to a pair of a shape operator and a metric. Therefore, we can define types of isoparametric hypersurfaces of index 2 concerning the classification. Secondly, we give several examples of certain types. Thirdly, we show that there exist no isoparametric hypersurfaces of index 2 whose shape operators have complex principal curvatures in certain cases. 2020 Mathematics Subject Classification. 53B30.

A theory of geometric continuity of arbitrary order is presented. Conditions of geometric continuity at a vertex where a number of patches meet are investigated. Geometric continuous patch complexes are introduced as the appropriate setting for the representation of surfaces in CAGD. The theory is applied to the modelling of closed surfaces and the fitting of triangular patches into a geometric continuous patch complex.

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