Ricci and Casorati principal directions of Chen ideal submanifolds
Simona Decu, Anica Pantić, Miroslava Petrović-Torgašev, Leopold Verstraelen (2013)
Kragujevac Journal of Mathematics
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Simona Decu, Anica Pantić, Miroslava Petrović-Torgašev, Leopold Verstraelen (2013)
Kragujevac Journal of Mathematics
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Chen, Bang-Yen (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Ryszard Deszcz, Miroslava Petrović-Torgašev, Zerrin Şentürk, Leopold Verstraelen (2010)
Publications de l'Institut Mathématique
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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...
Shichang, Shu, Sanyang, Liu (2004)
Balkan Journal of Geometry and its Applications (BJGA)
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Arslan, Kadri, Ezentas, Ridvan, Mihai, Ion, Murathan, Cengizhan, Özgür, Cihan (2002)
International Journal of Mathematics and Mathematical Sciences
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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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Franki Dillen, Johan Fastenakels (2009)
Open Mathematics
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We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.
Gupta, Ram Shankar, Haider, S.M.Khrusheed, Sharfuddin, A. (2006)
Balkan Journal of Geometry and its Applications (BJGA)
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