TY - JOUR AU - Chen, Bang-Yen PY - 2014/03/30 Y2 - 2024/03/29 TI - Some open problems and conjectures on submanifolds of finite type: recent development JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 45 IS - 1 SE - Papers DO - 10.5556/j.tkjm.45.2014.1564 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/1564 SP - 87-108 AB - 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]. ER -