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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2017.1
- 수록면
- 571 - 585 (15page)
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초록· 키워드
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Let $M$ be a connected $n$-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and $\Delta$ its Laplacian.
If the position vector $x$ of $M$ is decomposed as a sum of three vectors $x=x_1 + x_2 + x_0$where two vectors $x_1 $ and $x_2 $ are non-constant eigen vectors of the Laplacian , i.e., $\Delta x_i = \lambda_i x_i , i=1,2$ ( $\lambda_i \in R $) and $x_0$ is a constant vector, then, $M$ is called a 2-type submanifold.
In this paper we showed that a 2-type surface $M$ in $E^3$ satisfies $\langle \Delta x, x-x_0 \rangle = c$ for a constant $c$,where $\langle~, ~\rangle$ is the usual inner product in $E^3$, then $M$ is an open part of a circularcylinder. Also we showed that if a quadric hypersurface $M$ in a Euclidean space satisfies$\langle \Delta x, x \rangle = c$ for a constant $c$, then it is one of a minimal quadric hypersurface, a genaralized cone , a hypersphere, anda spherical cylinder.
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참고문헌 (5)
참고문헌 신청
B.-Y. Chen / 1984 / Total Mean Curvature and Submanifolds of Finite Type / World Scientific
B.-Y. Chen / 1988 / Null 2-type surfaces in E3 are circular cylinders / Kodai Math. J 11 : 295 ~ 299
B.-Y. Chen / 1992 / Quadric hypersurfaces of finite type / Colloq. Math 63 (2) : 145 ~ 152
Th. Hasanis / 1991 / Spherical 2-type hypersurface / J. Geom 40 : 82 ~ 94
Th. Hasanis / 1991 / a local classification of 2-type surfaces in S3 / Proc. Amer. Math. Soc 112 (2) : 533 ~ 538
B.-Y. Chen / 1988 / Null 2-type surfaces in E3 are circular cylinders / Kodai Math. J 11 : 295 ~ 299
B.-Y. Chen / 1992 / Quadric hypersurfaces of finite type / Colloq. Math 63 (2) : 145 ~ 152
Th. Hasanis / 1991 / Spherical 2-type hypersurface / J. Geom 40 : 82 ~ 94
Th. Hasanis / 1991 / a local classification of 2-type surfaces in S3 / Proc. Amer. Math. Soc 112 (2) : 533 ~ 538
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