Complete space-like submanifolds with constant scalar curvature in a de Sitter space.
Shichang, Shu, Sanyang, Liu (2004)
Balkan Journal of Geometry and its Applications (BJGA)
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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.
Ghazal, Tahsin, Deshmukh, Sharief (1991)
International Journal of Mathematics and Mathematical Sciences
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Ki, U-Hang, Kim, Young Ho (1996)
International Journal of Mathematics and Mathematical Sciences
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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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Cioroboiu, Dragoş (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Qing-ming Cheng (1991)
Mathematische Zeitschrift
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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.
Tripathi, Muck Main, Kim, Jean-Sic, Kim, Son-Be (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Simona Costache, Iuliana Zamfir (2014)
Annales Polonici Mathematici
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B. Y. Chen [Arch. Math. (Basel) 74 (2000), 154-160] proved a geometrical inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature. Recently, this Chen-Ricci inequality was improved in [Int. Electron. J. Geom. 2 (2009), 39-45]. On the other hand, K. Arslan et al. [Int. J. Math. Math. Sci. 29 (2002), 719-726] established a Chen-Ricci inequality for submanifolds, in particular in contact slant submanifolds,...
Li, Haizhong (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Vladimir Rovenski (2005)
Annales Polonici Mathematici
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We introduce and study submanifolds with extrinsic curvature and second fundamental form related by an inequality that holds for isotropic submanifolds and becomes equality for totally umbilical submanifolds. The dimension of umbilical subspaces and the index of conformal nullity of these submanifolds with low codimension are estimated from below. The corollaries are characterizations of extrinsic spheres in Riemannian spaces of positive curvature.
Bashir, M.A. (1995)
International Journal of Mathematics and Mathematical Sciences
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Alfonso Romero, Luis J. Alías (1995)
Manuscripta mathematica
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