Developable Complex Analytic Submanifolds

Examples of developable submanifolds are difficult to come by. For this reason, we collect in Sec. 1 some examples. There is one due to Cayley [2] that may not be so well-known, and there is also a new one which is algebraic. A knowledge of these examples is not essential for the subsequent sections, however. The organisation of the remainder of this paper is self-explanatory from the table of contents, except to mention that Sec. 7 contains the precise statements and proofs of Theorems 4–6. This paper and Sec. 2 of the paper [8] of Griffiths and Harris treat the same topic, although the latter is mainly interested in developable submanifolds in projective space. The discerning reader would note that our outlook and emphasis are orthogonal to those of [8] and that there are more differences than similarities between these two works.