### Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

Gupta, Ram Shankar, Haider, S.M.Khrusheed, Sharfuddin, A. (2006)

Balkan Journal of Geometry and its Applications (BJGA)

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Gupta, Ram Shankar, Haider, S.M.Khrusheed, Sharfuddin, A. (2006)

Balkan Journal of Geometry and its Applications (BJGA)

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Qing-ming Cheng (1991)

Mathematische Zeitschrift

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Bang-Yen Chen, Huei-Shyong Lue (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Haesen, Stefan, Verpoort, Steven (2010)

Beiträge zur Algebra und Geometrie

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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...

Qing-Ming Cheng (2005)

Banach Center Publications

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This paper is a survey of results on topological structures and curvature structures of complete submanifolds in a Euclidean space.

Lohkamp, Joachim (1998)

Documenta Mathematica

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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.

Christos Baikoussis, Themis Koufogiorgos (1988)

Colloquium Mathematicae

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Wolfgang Kühnel (1979)

Colloquium Mathematicae

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P. J. De Smet, F. Dillen, Leopold C. A. Verstraelen, L. Vrancken (1999)

Archivum Mathematicum

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We obtain a pointwise inequality valid for all submanifolds ${M}^{n}$ of all real space forms ${N}^{n+2}\left(c\right)$ with $n\ge 2$ 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 ${N}^{m}\left(c\right)$.