Matches in SemOpenAlex for { <https://semopenalex.org/work/W2134347681> ?p ?o ?g. }
- W2134347681 abstract "A hypersurface M n 1 in a real space-form R n , S n or H n is isoparametric if it has constant principal curvatures. For R n and H n , the classification of isoparametric hypersurfaces is complete and relatively simple, but as ´ Elie Cartan showed in a series of four papers in 1938-1940, the subject is much deeper and more complex for hypersurfaces in the sphere S n . A hypersurface M n 1 in a real space-form is proper Dupin if the number g of distinct principal curvatures is constant on M n 1 , and each principal curvature function is constant along each leaf of its corresponding principal foliation. This is an important genera- lization of the isoparametric property that has its roots in nineteenth century differential geometry and has been studied effectively in the context of Lie sphere geometry. This paper is a survey of the known results in these fields with emphasis on results that have been obtained in more recent years and discussion of important open problems in the field." @default.
- W2134347681 created "2016-06-24" @default.
- W2134347681 creator A5042605317 @default.
- W2134347681 date "2008-09-08" @default.
- W2134347681 modified "2023-10-13" @default.
- W2134347681 title "Isoparametric and Dupin Hypersurfaces" @default.
- W2134347681 cites W118189009 @default.
- W2134347681 cites W1420538528 @default.
- W2134347681 cites W1482911014 @default.
- W2134347681 cites W1503695036 @default.
- W2134347681 cites W1513885689 @default.
- W2134347681 cites W1514674107 @default.
- W2134347681 cites W1521626780 @default.
- W2134347681 cites W1524224706 @default.
- W2134347681 cites W1525991586 @default.
- W2134347681 cites W1530500087 @default.
- W2134347681 cites W1534817776 @default.
- W2134347681 cites W1547048629 @default.
- W2134347681 cites W1550317776 @default.
- W2134347681 cites W1552161690 @default.
- W2134347681 cites W1552847376 @default.
- W2134347681 cites W1553459633 @default.
- W2134347681 cites W1553674561 @default.
- W2134347681 cites W1554149356 @default.
- W2134347681 cites W1555186976 @default.
- W2134347681 cites W15603573 @default.
- W2134347681 cites W1565709665 @default.
- W2134347681 cites W1566596520 @default.
- W2134347681 cites W1568100409 @default.
- W2134347681 cites W1568295503 @default.
- W2134347681 cites W1575293772 @default.
- W2134347681 cites W157927367 @default.
- W2134347681 cites W1583911619 @default.
- W2134347681 cites W1584769248 @default.
- W2134347681 cites W1585928768 @default.
- W2134347681 cites W1587069887 @default.
- W2134347681 cites W1595797002 @default.
- W2134347681 cites W1596528476 @default.
- W2134347681 cites W1602656968 @default.
- W2134347681 cites W1728942627 @default.
- W2134347681 cites W1776436775 @default.
- W2134347681 cites W1935132094 @default.
- W2134347681 cites W1965105415 @default.
- W2134347681 cites W1965982184 @default.
- W2134347681 cites W1971033131 @default.
- W2134347681 cites W1973105701 @default.
- W2134347681 cites W1973673932 @default.
- W2134347681 cites W1974869406 @default.
- W2134347681 cites W1976469870 @default.
- W2134347681 cites W1982170949 @default.
- W2134347681 cites W1982537419 @default.
- W2134347681 cites W1984417688 @default.
- W2134347681 cites W1985052947 @default.
- W2134347681 cites W1987632147 @default.
- W2134347681 cites W1989775132 @default.
- W2134347681 cites W1989794053 @default.
- W2134347681 cites W1991688263 @default.
- W2134347681 cites W1996216630 @default.
- W2134347681 cites W1997936382 @default.
- W2134347681 cites W2007909305 @default.
- W2134347681 cites W2008486048 @default.
- W2134347681 cites W2008799033 @default.
- W2134347681 cites W2009598464 @default.
- W2134347681 cites W2009962042 @default.
- W2134347681 cites W201339904 @default.
- W2134347681 cites W2013798651 @default.
- W2134347681 cites W2014665523 @default.
- W2134347681 cites W2016359862 @default.
- W2134347681 cites W2018070337 @default.
- W2134347681 cites W2018351175 @default.
- W2134347681 cites W2020538077 @default.
- W2134347681 cites W2022055730 @default.
- W2134347681 cites W2024581708 @default.
- W2134347681 cites W2027594107 @default.
- W2134347681 cites W2033659189 @default.
- W2134347681 cites W2034292086 @default.
- W2134347681 cites W2035267725 @default.
- W2134347681 cites W2035898622 @default.
- W2134347681 cites W2039108329 @default.
- W2134347681 cites W2040736577 @default.
- W2134347681 cites W2041309932 @default.
- W2134347681 cites W2042371078 @default.
- W2134347681 cites W2044501984 @default.
- W2134347681 cites W2046487977 @default.
- W2134347681 cites W2050223434 @default.
- W2134347681 cites W2051405205 @default.
- W2134347681 cites W2052841982 @default.
- W2134347681 cites W2053276217 @default.
- W2134347681 cites W2054770659 @default.
- W2134347681 cites W2056424701 @default.
- W2134347681 cites W2056678281 @default.
- W2134347681 cites W2060878503 @default.
- W2134347681 cites W2062100093 @default.
- W2134347681 cites W2063921502 @default.
- W2134347681 cites W2064251653 @default.
- W2134347681 cites W2065876525 @default.
- W2134347681 cites W2074772450 @default.
- W2134347681 cites W2076002049 @default.
- W2134347681 cites W2079773617 @default.
- W2134347681 cites W2085413555 @default.