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- Shichang Shu, Annie Yi Han
- 2009

Let M be an n(n ≥ 3)-dimensional complete connected hyper-surface in a unit sphere S n+1 (1). In this paper, we show that (1) if M has non-zero mean curvature and constant scalar curvature n(n − 1)r and two distinct principal curvatures, one of which is simple, then M is isometric to the Riemannian product S 1 (√ 1 − c 2) × S n−1 (c), c 2 = n−2 nr if r ≥… (More)

- Shichang Shu
- Ars Comb.
- 2013

- Junfeng Chen, Shichang Shu
- 2012

We study some Weingarten spacelike hypersurfaces in a de Sitter space S n+1 1 (1). If the Weingarten spacelike hypersurfaces have two distinct principal curvatures, we obtain two classification theorems which give some characterization of the Riemannian product H k (1−coth 2 ̺)× S n−k (1 − tanh 2 ̺), 1 < k < n − 1 in S n+1 1 (1), the hyperbolic cylinder H 1… (More)

- SHICHANG SHU, SANYANG LIU
- 2011

Let M be an n-dimensional compact Willmore Lagrangian submanifold in a complex projective space CP n and let S and H be the squared norm of the second fundamental form and the mean curvature of M. Denote by ρ 2 = S − nH 2 the non-negative function on M , K and Q the functions which assign to each point of M the infimum of the sectional curvature and Ricci… (More)

- Shichang Shu
- 2017

For a given (n − 1)-dimensional hypersurface x : M → R, consider the Laguerre form Φ, the Laguerre tensor L and the Laguerre second fundamental form B of the immersion x. In this article, we address the case when the Laguerre form of x is parallel, i.e., ∇Φ ≡ 0. We prove that ∇Φ ≡ 0 is equivalent to Φ ≡ 0, provided that either L+λB+μg = 0 for some smooth… (More)

- Shichang Shu, Tianmin Zhu
- 2015

In this paper, we would like to study space-like submanifolds in a de Sitter spaces S p (1). We define and discuss three Schrödinger operators LH , LR, LR/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators LH , LR and LR/H respectively.

- SHICHANG SHU, YANYAN LI
- 2011

In this paper, we investigate n-dimensional submanifolds with higher codimension in a unit sphere Sn+p(1). We obtain some rigidity results of submanifolds in Sn+p(1) with parallel mean curvature vector or with constant scalar curvature, which generalize some related rigidity results of hypersurfaces.

- Junfeng Chen, Shichang Shu
- Int. J. Math. Mathematical Sciences
- 2014

- Shichang Shu, Junfeng Chen
- 2015

In this paper, we study the conformal geometry of conformal isoparametric spacelike hypersurfaces in conformal space Q n+1 1. We obtain the classification of the conformal isoparametric spacelike hypersurfaces in Q n+1 1 with three distinct conformal principal curvatures, one of which is simple, and the classification of the conformal isoparametric… (More)

- Shichang Shu, Junfeng Chen
- 2014

Let N n+p p (c) be an (n+p)-dimensional connected Lorentzian space form of constant sectional curvature c and φ : M → N n+p p (c) an n-dimensional spacelike submanifold in N n+p p (c). The immersion φ : M → N n+p p (c) is called a Willmore spacelike submanifold in N n+p p (c) if it is a critical submanifold to the Willmore functional W (φ) = ∫ M ρ n dv = ∫… (More)