Abstract
The general theory of surfaces has been developed without much attention to the simpler aspects of the subject and, in particular, to the problem of determining some elementary criteria of regularity or referability; there is, in fact, only one well-known criterion of this kind, due to Castelnuovo and Enriques. (Theorem 2 of the present work.) It seems desirable, therefore, to establish some tests which require no more knowledge of a surface than its order, sectional genus and normal space. A number of such tests is given in the present paper. Before it was written the author had the advantage of consulting an unpublished manuscript by Professor Comessatti on the classification of surfaces in S4; in this work the regularity of surfaces of order eight is considered and, in part, those of order nine; the four-dimensional case of Theorem 11 and a particular case of Theorem 6 and Theorem 14 are given. Theorems 4 and 5 are also proved by Comessatti. For permission to publish these results and for the help derived from them the author's grateful thanks are due.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Mathematical Proceedings of the Cambridge Philosophical Society
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.