New approach for the submanifolds of the Euclidean space.
Trenčevski, K. (1997)
Balkan Journal of Geometry and its Applications (BJGA)
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Trenčevski, K. (1997)
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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Tripathi, Muck Main, Kim, Jean-Sic, Kim, Son-Be (2002)
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 (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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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,...
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.
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.
Alfonso Romero, Luis J. Alías (1995)
Manuscripta mathematica
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Li, Haizhong (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Bashir, M.A. (1995)
International Journal of Mathematics and Mathematical Sciences
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Stanisław Ewert-Krzemieniewski (2010)
Colloquium Mathematicae
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We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.