A sharp characterization of the Willmore invariant
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1142/S0129167X23500544 |
| Doi | http://dx.doi.org/10.1142/S0129167X23500544 |
| Keywords | Extrinsic conformal geometry; hypersurface embeddings; Willmore invariant |
| Description | First introduced to describe surfaces embedded in R3, the Willmore invariant is a conformally-invariant extrinsic scalar curvature of a surface that vanishes when the surface minimizes bending and stretching. Both this invariant and its higher-dimensional analogs appear frequently in the study of conformal geometric systems. To that end, we provide a characterization of the Willmore invariant in general dimensions. In particular, we provide a sharp sufficient condition for the vanishing of the Willmore invariant and show that in even dimensions it can be described fully using conformal fundamental forms and one additional tensor. |
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