Biharmonic curves into quadrics

Abstract

We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular, we use it to give a complete classification of biharmonic curves into real quadrics of the 3-dimensional Euclidean space.

10 pages

References in corpus (1)

• Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group

Cited by in corpus (2)

• Some open problems and conjectures on submanifolds of finite type: recent development
• Biharmonic submanifolds into ellipsoids