Some open problems and conjectures on submanifolds of finite type: recent development

Authors

  • Bang-Yen Chen Department of Mathematic, Michigan State University

DOI:

https://doi.org/10.5556/j.tkjm.45.2014.1564

Keywords:

Finite type submanifold, biharmonic submanifold, biharmonic conjecture, Chen's conjecture, linearly independent immersion, orthogonal immersion.

Abstract

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].

Author Biography

Bang-Yen Chen, Department of Mathematic, Michigan State University

Department of Mathematics,MichiganStateUniversity

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2014-03-30

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Chen, B.-Y. (2014). Some open problems and conjectures on submanifolds of finite type: recent development. Tamkang Journal of Mathematics, 45(1), 87-108. https://doi.org/10.5556/j.tkjm.45.2014.1564

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