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A characterization of the Ejiri torus in S 5
- Source :
- Acta Mathematica Sinica, English Series. 32:1014-1026
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- We conjecture that a Willmore torus having Willmore functional between 2π 2 and 2π 2 $$\sqrt 3 $$ is either conformally equivalent to the Clifford torus, or conformally equivalent to the Ejiri torus. Ejiri’s torus in S 5 is the first example of Willmore surface which is not conformally equivalent to any minimal surface in any real space form. Li and Vrancken classified all Willmore surfaces of tensor product in S n by reducing them into elastic curves in S 3, and the Ejiri torus appeared as a special example. In this paper, we first prove that among all Willmore tori of tensor product, the Willmore functional of the Ejiri torus in S 5 attains the minimum 2π 2 $$\sqrt 3 $$ , which indicates our conjecture holds true for Willmore surfaces of tensor product. Then we show that all Willmore tori of tensor product are unstable when the co-dimension is big enough. We also show that the Ejiri torus is unstable even in S 5. Moreover, similar to Li and Vrancken, we classify all constrained Willmore surfaces of tensor product by reducing them with elastic curves in S 3. All constrained Willmore tori obtained this way are also shown to be unstable when the co-dimension is big enough.
- Subjects :
- Pure mathematics
Minimal surface
Conjecture
010308 nuclear & particles physics
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Space form
Clifford torus
Torus
Surface (topology)
01 natural sciences
Willmore energy
Tensor product
0103 physical sciences
Mathematics::Differential Geometry
0101 mathematics
Mathematics::Symplectic Geometry
Mathematics
Subjects
Details
- ISSN :
- 14397617 and 14398516
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Acta Mathematica Sinica, English Series
- Accession number :
- edsair.doi...........951916aee50232c4b32705f3120c39a3