• Honam Mathematical Journal
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• v.28 no.1
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• pp.141-164
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• 2006

Let $G=O(2){\times}O(2){\times}O(2)$ and let $M^4$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$. In this paper, we prove a property on $M^4$.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.113-132
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• 2001

We prove an equality that holds on G-invariant minimal hypersurfaces with constant scalar curvatures in $S^5$.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.381-398
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• 2009

Let $G\;=\;O(k){\times}O(k){\times}O(q)$ and let $M^n$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^{n+1}$. Then we obtain a theorem: If $M^n$ has 2 distinct principal curvatures at some point p, then the square norm of the second fundamental form of $M^n$, S = n.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.261-278
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• 2002

Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.515-540
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• 2013

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).