ICTS

During the last two decades, the study of biharmonic submanifolds has been an active area of research. It is well-known that the conjecture made by Chen in 1991 that "The only biharmonic submanifolds of Euclidean spaces are the minimal ones" is still an open problem. We have proved some important results to validate and generalize the Chen's conjecture in different ambient spaces such as Euclidean space, pseudo-Euclidean space and space form. Also, author will investigate and classify the biconservative submanifolds as a natural generalization of biharmonic submanifolds in the presentation.