본문 바로가기
KERD
논문KCI 등재

Linear Weingarten hypersurfaces in a unit sphere

서영진|Haizhong Li|Guoxin Wei
대한수학회 (The Korean Mathematical Society)|2009.03|대한수학회보 (Bulletin of the KMS)|제46권 제2호|pp. 321-329

0

조회

0

다운로드

4

인용

0

참고문헌

키워드

linear Weingarten hypersurfacesrigidity theoremsCheng-Yau differential operator
주제분류수학

초록

In this paper, we have considered linear Weingarten hypersurfaces in a sphere and obtained some rigidity theorems. The purpose of this paper is to give some extension of the results due to Cheng-Yau [3] and Li [7].

Abstract

In this paper, we have considered linear Weingarten hypersurfaces in a sphere and obtained some rigidity theorems. The purpose of this paper is to give some extension of the results due to Cheng-Yau [3] and Li [7].

참고문헌 (12)

  1. ´E. Cartan, "amilles de surfaces isoparam´etriques dans les espaces `a courbure constante", Ann. Mat. Pura Appl, 17(1), pp.177~191 (1938)
  2. Q. M. Cheng, "Hypersurfaces in a unit sphere Sn+1(1) with constant scalar curvature", J. London Math. Soc., 64(3), pp.755~768 (2001)
  3. S. Y. Cheng, "Hypersurfaces with constant scalar curvature", 195–204., 225(3), pp.195~204 (1977)
  4. S. S. Chern, "Some new characterizations of the Euclidean sphere", Duke Math. J., 12, pp.279~290 (1945)
  5. S. S. Chern, "Minimal submanifolds of a sphere with second fundamental form of constant length", Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968), pp.59~75 (1970), Springer
  6. H. Li, "Hypersurfaces with constant scalar curvature in space forms", Math. Ann., 305(4), pp.665~672 (1996)
  7. H. Li, "Global rigidity theorems of hypersurfaces", Ark. Mat., 35(2), pp.327~351 (1997)
  8. K. Nomizu, "A formula of Simons’ type and hypersurfaces with constant mean curvature", J. Differential Geometry, 3, pp.367~377 (1969)
  9. M. Okumura, "Hypersurfaces and a pinching problem on the second fundamental tensor", Amer. J. Math., 96, pp.207~213 (1974)
  10. Y. J. Suh, "On space-like hypersurfaces with constant mean curvature in a Lorentz manifold", Houston J. Math., 28(1), pp.47~70 (2002)
  11. Y. J. Suh, "The scalar curvature of minimal hypersurfaces in a unit sphere", Contemp. Math, 9(2), pp.183~200 (2007)
  12. G.Wei, "Rigidity theorem for hypersurfaces in a unit sphere", Monatsh. Math., 149(4), pp.343~350 (2006)

관련 논문AI추천

Linear Weingarten hypersurfaces in Riemannian space formsPeijun Wang, Xiaoli Chao대한수학회 · 대한수학회보2014 · 제51권 제2호Hypersurfaces with constant $\boldsymbol{k}$-th mean curvature and two distinct principal curvatures in spheresJiancheng Liu, Yan Wei대한수학회 · 대한수학회보2012 · 제49권 제2호Elliptic Linear Weingarten Surfaces김영호경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제3호LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACEDan Yang대한수학회 · 대한수학회보2012 · 제49권 제2호On Yau rigidity theorem for submanifolds with parallel mean curvature in a locally symmetric Riemannian manifoldFei Yang대한수학회 · 대한수학회보2024 · 제61권 제5호The rigidity of minimal submanifolds in a locally symmetric spaceShunjuan Cao대한수학회 · 대한수학회보2013 · 제50권 제1호

이 간행물의 다른 논문 (18건)

The nearly additive mapsNasrin Eghbali, Esmaeeil Ansari-Piripp. 199-207Comparison of stochastic volatility models: Empirical study on KOSPI 200 index optionsChoongseok Yoon, 위인숙, 문경숙, Jung-Yon Seonpp. 209-227Congruences for coefficients of Drinfeld modular forms최소영pp. 229-234Notes on the superstability of d'Alembert type functional equationsBing Xu, Peng Caopp. 235-243Analysis of the strong instance for the vector decomposition problem이향숙, 권세란pp. 245-253
원문 보기