Indefinite extrinsic spheres (Q1002473)

The paper deals with the intersection \(M\) of an algebraic hypersurface \(\tilde M\) and a pseudoshere \(S\) of the complex space \(C^n_s\) equipped with an indefinite quadratic form with signature \( (s,n-s)\). In the positive definite case \((s=0)\) the intersection \(M\) turns out to be an example of an extrinsic sphere. The authors study the geometry of the second fundamental form of \(M\) both in \(\tilde M\) and in \(C^n_s\).