The fundamental theorems for affine immersions into hyperquadrics and applications (Q1841251)

The author proves the fundamental theorems (i.e. existence and equivalence theorem) for affine immersions in the sense of Nomizu-Sasaki into (nondegenerate) hyperquadrics (including affine spaces) with arbitrary codimension. As application to special cases he obtains the known fundamental theorems for affine immersions into affine spaces as well as for isometric immersions into space forms. Another application yields Koike's fundamental theorems for his equiaffine immersions into hyperquadrics with arbitrary codimension.