Variational problems of total mean curvature of submanifolds in a sphere
Copyright policy )Variational problems of total mean curvature of submanifolds in a sphere
Let H \mathbf {H} be the mean curvature vector of an n n -dimensional submanifold in a Riemannian manifold. The functional H = ∫ ‖ H ‖ n \mathcal {H}=\int \|\mathbf {H}\|^{n} is called the total mean curvature functional. In this paper, we present the first variational formula of H \mathcal {H} and then, for a critical surface of H \mathcal {H} in the ( 2 + p 2+p )-dimensional unit sphere S 2 + p \mathbb {S}^{2+p} , we establish the relationship between the integral of an extrinsic quantity of the surfaces and its Euler characteristic number.
- Yunnan Normal University China (People's Republic of)
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Global submanifolds, total mean curvature, Euler characteristic, variation, Sub-Riemannian geometry, submanifolds
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Global submanifolds, total mean curvature, Euler characteristic, variation, Sub-Riemannian geometry, submanifolds
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