논문KCI 등재
On G-invariant Minimal Hypersurfaces with Constant Scalar Curvatures in S5
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Let G = O(2)xO(2)xO(2). Then a closed G-invariant minimal hypersurfacewith constant scalar curvature in S5 is a product of spheres, i.e., the square norm of itssecond fundamental form, S = 4.
Abstract
Let G = O(2)xO(2)xO(2). Then a closed G-invariant minimal hypersurfacewith constant scalar curvature in S5 is a product of spheres, i.e., the square norm of itssecond fundamental form, S = 4.
참고문헌 (9)
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- S. S. Chern, "M. do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length", Duke Math. J., 61, pp.195~206 (1990)
- W. Y. Hsiang, "On the construction of in nitely many congruence classes of imbedded closed minimal hypersurfaces in Sn(1) for all n 3", Duke Math. J., 55(2), pp.361~367 (1987)
- H. B. Lawson, "Local rigidity theorems for minimal hypersurfaces", Annals of Math., 89, pp.187~191 (1969)
- C. K. Peng, "Minimal hypersurface of spheres with constant scalar curvature", pp.177~198 (1983), Princeton University Press
- J. Simons, "Minimal varieties in a Riemannian manifold", Ann. of Math., 88, pp.62~105 (1968)
- 소재업, "On G-invariant minimal hypersurfaces with constant scalar curvature in S^5", 대한수학회논문집, 17(2), pp.261~278 (2002), 대한수학회
- H. Yang, "Chern's conjecture on minimal hypersurfaces", Math. Z, 227, pp.377~390 (1998)
- S. T. Yau, "Problem section", pp.693~ (1982), Princeton University Press
관련 논문AI추천
On G-invariant minimal hypersurfaces with constant scalar curvature in S^5소재업대한수학회 · 대한수학회논문집2002 · 제17권 제2호Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces서검교대한수학회 · 대한수학회보2011 · 제48권 제2호Biharmonic Hypersurfaces with Constant Scalar Curvature in E5sA. Sharfuddin, Deepika, Ram Shankar Gupta경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호Hypersurfaces with constant $\boldsymbol{k}$-th mean curvature and two distinct principal curvatures in spheresJiancheng Liu, Yan Wei대한수학회 · 대한수학회보2012 · 제49권 제2호The rigidity of minimal submanifolds in a locally symmetric spaceShunjuan Cao대한수학회 · 대한수학회보2013 · 제50권 제1호Minimal and Constant mean curvature surfaces in $\mathbb S^3$ foliated by circles박성호대한수학회 · 대한수학회보2019 · 제56권 제6호
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