Free elasticae and Willmore tori in warped product spaces
نویسندگان
چکیده
منابع مشابه
Willmore-chen Tubes on Homogeneous Spaces in Warped Product Spaces
We present a new method to obtain Willmore-Chen submanifolds in spaces endowed with warped product metrics and fibers being a given homogeneous space. The main points are: First the invariance of the variational problem of WillmoreChen with respect to the conformal changes in the ambient space metric. Second, the principle of symmetric criticality which allows us to relate the problem with that...
متن کاملNew Examples of Willmore Tori in S4
Using the (generalized) Darboux transformation in the case of the Clifford torus, we construct for all Pythagorean triples (p, q, n) ∈ Z a CP–family of Willmore tori in S with Willmore energy 2nπ.
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملInterpolations with Elasticae in Euclidean Spaces
Motivated by interpolation problems arising in image analysis, computer vision, shape reconstruction and signal processing, we develop an algorithm to simulate curve straightening flows under which curves in R of fixed length and prescribed boundary conditions to first order evolve to elasticae, i.e., to (stable) critical points of the elastic energy E given by the integral of the square of the...
متن کاملA Gap Theorem for Willmore Tori and an Application to the Willmore Flow
In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2 and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves in [13]. In this paper, we show for tori there is a gap to the next critical point of the Willmore energy and we discuss an a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1998
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500032596