Null 2-type space-like submanifolds of with normalized parallel mean curvature vector.
Dursun, Uǧur (2006)
Balkan Journal of Geometry and its Applications (BJGA)
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Dursun, Uǧur (2006)
Balkan Journal of Geometry and its Applications (BJGA)
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Qing-ming Cheng (1991)
Mathematische Zeitschrift
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Shichang, Shu, Sanyang, Liu (2004)
Balkan Journal of Geometry and its Applications (BJGA)
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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.
Maria Helena Noronha (1991)
Manuscripta mathematica
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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 of all real space forms with and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of in .
Ghazal, Tahsin, Deshmukh, Sharief (1991)
International Journal of Mathematics and Mathematical Sciences
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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...
Bang-Yen Chen, Huei-Shyong Lue (1988)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Helmut Reckziegel (1974)
Manuscripta mathematica
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