Ovaloids of R3 and their umbilics:: A differential equation approach

[摘要] The following extension of the Caratheodory conjecture on umbilies is proposed and solved-in very special cases: Let N: M --> S-2 be the Gauss map of a C-3 ovaloid M subset of R-3. Let A be the set of umbilies q epsilon M such that N(q) = q. If A is a connected component of sl, then, each connected component or M\A contains at least an umbilic point of M. (C) 2000 Academic Press.

[发布日期] 2000-11-20

[关键词] umbilic point;principal lilies;Caratheodory conjecture