During the last four decades, there were numerous important developments on total mean
curvature and the theory of finite type submanifolds. This unique and expanded second …

In this note, we give a brief survey on some recent developments of biharmonic
submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the …

We present some general properties of biharmonic and biconservative submanifolds and
then survey recent results on such hypersurfaces in space forms. We also propose an …

A submanifold $ M $ of a Euclidean $ m $-space is said to be biharmonic if
$\Delta\overrightarrow H= 0$ holds identically, where $\overrightarrow H $ is the mean …

Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor |
Annali di Matematica Pura ed Applicata (1923 -) Skip to main content SpringerLink Account …

A longstanding conjecture on biharmonic submanifolds, proposed by Chen in 1991, is that
any biharmonic submanifold in a Euclidean space is minimal. In the case of a hypersurface …

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 …

We obtain several rigidity results for biharmonic submanifolds in S^n with parallel
normalized mean curvature vector fields. We classify biharmonic submanifolds in S^n with …

The position vector field is the most elementary and natural geometric object on a Euclidean
submanifold. The purpose of this article is to survey six research topics in differential …

We give some general results on proper-biharmonic submanifolds of a complex space form
and, in particular, of the complex projective space. These results are mainly concerned with …