지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
이용수
초록· 키워드
오류제보하기
In 1997, H. Li {\cite{Li97}} proposed a conjecture: if $M^{n} (n\geqslant3)$ is a complete spacelike hypersurface in de Sitter space $S_{1}^{n+1}(1)$ with constant normalized scalar curvature $R$ satisfying $\frac{n-2}{n}\leqslant R\leqslant1$, then is $M^{n}$ totally umbilical? Recently, F.~E.~C.~Camargo et al.~(\cite{Camargo08}) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^{n}$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^{n}$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^{n}$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^{n}$ in locally symmetric Lorentz space $L_{1}^{n+1}$ satisfies $K(M^{n})>0$, then $M^{n}$ is totally umbilical, i.e., Theorem 2.
목차
등록된 정보가 없습니다.
참고문헌 (19)
참고문헌 신청
A. Brasil Jr. / 2001 / A gap theorem for complete constant scalar curvature hypersurfaces in the De Sitter space / J. Geom. Phys 37 (3) : 237 ~ 250
A. J. Goddard / 1977 / Some remarks on the existence of spacelike hypersurfaces of constant mean curvature / Math. Proc. Cambridge Philos. Soc 82 (3) : 489 ~ 495
F. E. C. Camargo / 2008 / Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in de Sitter space / Dif-ferential Geom. Appl 26 (6) : 592 ~ 5
H. Alencar / 1994 / Hypersurfaces with constant mean curvature in spheres / Proc. Amer. Math. Soc 120 (4) : 1223 ~ 1229
H. Li / 1997 / Global rigidity theorems of hypersurfaces / Ark. Mat 35 (2) : 327 ~ 351
A. J. Goddard / 1977 / Some remarks on the existence of spacelike hypersurfaces of constant mean curvature / Math. Proc. Cambridge Philos. Soc 82 (3) : 489 ~ 495
F. E. C. Camargo / 2008 / Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in de Sitter space / Dif-ferential Geom. Appl 26 (6) : 592 ~ 5
H. Alencar / 1994 / Hypersurfaces with constant mean curvature in spheres / Proc. Amer. Math. Soc 120 (4) : 1223 ~ 1229
H. Li / 1997 / Global rigidity theorems of hypersurfaces / Ark. Mat 35 (2) : 327 ~ 351
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Complete spacelike hypersurfaces with CMC in Lorentz Einstein manifolds
대한수학회보
2021 .09
-
Generalized golden shaped hypersurfaces in Lorentz space forms
대한수학회논문집
2016 .01
-
ON THE WEIERSTRASS THEOREM OF A MAXIMAL SPACELIKE SURFACE
East Asian Mathematical Journal
2017 .01
-
A sharp integral inequality for compact linear Weingarten hypersurfaces
대한수학회보
2022 .05
-
Notes on real hypersurfaces in a complex space form
대한수학회보
2015 .01
-
Lightlike hypersurfaces of a Lorentz manifold with a semi-symmetric non-metric connection
East Asian Mathematical Journal
2015 .01
-
On $\bH_2$-proper timelike hypersurfaces in Lorentz $4$-space forms
대한수학회논문집
2024 .07
-
Equivalence conditions of symmetry properties in lightlike hypersurfaces of indefinite Kenmotsu manifolds
대한수학회보
2016 .01
-
Real Hypersurfaces in a Nonflat Complex Space Form with Special Structure Tensor Field
순수 및 응용수학
2021 .08
-
Volume ratios of a hypersurface relative to the FLRW space-time
대한수학회논문집
2015 .01
-
Non-existance Real Hypersurfaces in a Nonflat Complex Space Form with Codazzi Type of Structure Tensor Field
순수 및 응용수학
2021 .01
-
Deforming pinched hypersurfaces of the hyperbolic space by powers of the mean curvature into spheres
대한수학회지
2016 .01
-
Almost rigidity of convex hypersurfaces via the extinction time of mean curvature flow
대한수학회보
2021 .01
-
Certain curvature conditions of real hypersurfaces in a complex hyperbolic space
대한수학회논문집
2015 .01
-
Myers' theorem for complete Riemannian hypersurfaces
대한수학회논문집
2019 .01
-
Some Results on Null Hypersurfaces in (LCS)-manifolds
Kyungpook Mathematical Journal
2019 .01
-
Biharmonic spacelike curves in Lorentzian Heisenberg space
대한수학회논문집
2018 .01
-
Lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection
대한수학회보
2015 .01
-
Lightlike hypersurfaces of an indefinite Kaehler manifold with a non-metric Φ-symmetric connection
대한수학회보
2017 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0