Stable 3-spheres in $\mathbb{C}^3$

Isabel M. C. Salavessa

Stable 3-spheres in $\mathbb{C}^3$

Differential Geometry 2012-01-11 v3

Authors: Isabel M. C. Salavessa

Abstract

By only using spectral theory of the Laplace operator on spheres, we prove that the unit 3-dimensional sphere of a 2-dimensional complex subspace of $\mathbb{C}^3$ is a $\Omega$ -stable submanifold with parallel mean curvature, when $\Omega$ is the K\"ahler calibration of rank 4 of $\mathbb{C}^3$ .

Keywords

surfaces and embeddings sphere packings and spherical designs

Cite

@article{arxiv.1111.3287,
  title  = {Stable 3-spheres in $\mathbb{C}^3$},
  author = {Isabel M. C. Salavessa},
  journal= {arXiv preprint arXiv:1111.3287},
  year   = {2012}
}

Comments

15 pages. v3: We add a reference of a pioneer and fundamental work due to Frank Morgan, explain its relation in the introduction, correct some typos and English grammar

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