Some 2-type submanifolds and applications

Bang-Yen Chen; Huei-Shyong Lue

Displaying similar documents to “Some 2-type submanifolds and applications”

Null 2-type space-like submanifolds of $E_{t}^{5}$ with normalized parallel mean curvature vector.

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Balkan Journal of Geometry and its Applications (BJGA)

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Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

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A pointwise inequality in submanifold theory

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Archivum Mathematicum

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We obtain a pointwise inequality valid for all submanifolds $M^{n}$ of all real space forms $N^{n + 2} (c)$ with $n \geq 2$ and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of $M^{n}$ , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of $M^{n}$ in $N^{m} (c)$ .

Totally real surfaces in $ℂ P^{2}$ with parallel mean curvature vector.

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International Journal of Mathematics and Mathematical Sciences

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Slant surfaces with prescribed Gaussian curvature.

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Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector.

Qing-ming Cheng (1991)

Mathematische Zeitschrift

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Non-degenerate quadric surfaces of Weingarten type

Dae Won Yoon, Yılmaz Tunçer, Murat Kemal Karacan (2013)

Annales Polonici Mathematici

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We study quadric surfaces in Euclidean 3-space with non-degenerate second fundamental form, and classify them in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature.

On some generalisations of constant mean curvature surfaces.

Fujioka, A., Inoguchi, J. (1999)

Lobachevskii Journal of Mathematics

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Global pinching theorems of submanifolds in spheres.

Cai, Kairen (2002)

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On the total (non absolute) curvature of a even dimensional submanifold X immersed in R.

A. M. Naveira (1994)

Revista Matemática de la Universidad Complutense de Madrid

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The total curvatures of the submanifolds immersed in the Euclidean space have been studied mainly by Santaló and Chern-Kuiper. In this paper we give geometrical and topological interpretation of the total (non absolute) curvatures of the even dimensional submanifolds immersed in R. This gives a generalization of two results obtained by Santaló.

A pinching theorem on complete submanifolds with parallel mean curvature vectors

Ziqi Sun (2003)

Colloquium Mathematicae

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Let M be an n-dimensional complete immersed submanifold with parallel mean curvature vectors in an (n+p)-dimensional Riemannian manifold N of constant curvature c > 0. Denote the square of length and the length of the trace of the second fundamental tensor of M by S and H, respectively. We prove that if S ≤ 1/(n-1) H² + 2c, n ≥ 4, or S ≤ 1/2 H² + min(2,(3p-3)/(2p-3))c, n = 3, then M is umbilical. This result generalizes the...