finite type submanifolds
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2014 ◽  
Vol 45 (1) ◽  
pp. 87-108 ◽  
Author(s):  
Bang-Yen Chen

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type submanifolds was published in [40]. A detailed survey of the results, up to 1996, on this subject was given by the author in [48]. Recently, the study of finite type submanifolds, in particular, of biharmonic submanifolds, have received a growing attention with many progresses since the beginning of this century. In this article, we provide a detailed account of recent development on the problems and conjectures listed in [40].


1994 ◽  
Vol 36 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Filip Defever ◽  
Ryszard Deszcz ◽  
Leopold Verstraelen

Minimal submanifolds of a Euclidean space are contained in a much larger class of submanifolds, namely in the class of submanifolds of finite type. Submanifolds of finite type were introduced about a decade ago by B. Y. Chen in [2]; the first results on this subject have been collected in the books [2], [3].


1991 ◽  
Vol 44 (3) ◽  
pp. 391-396
Author(s):  
Shi-Jie Li

The notion of finite type submanifolds was introduced by B.Y. Chen. In this article we study 2- and 3-type pseudo-umbilical submanifolds in a hypersphere. Two theorems in this respect are obtained.


1991 ◽  
Vol 37 (2) ◽  
Author(s):  
Thomas Hasanis ◽  
Theodore Vlachos

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