On the submanifolds of the Riemannian manifolds.
Trenčevski, K. (1999)
Novi Sad Journal of Mathematics
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Trenčevski, K. (1999)
Novi Sad Journal of Mathematics
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Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar (2016)
Annales Polonici Mathematici
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Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds...
Michael T. Anderson, Lucio Rodriguez (1989)
Mathematische Annalen
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Li, Haizhong (1993)
Publications de l'Institut Mathématique. Nouvelle Série
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Catherine Searle (1993)
Mathematische Zeitschrift
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Hukum Singh (1985)
Publications de l'Institut Mathématique
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Y.Y. Baldin, Maria H. Noronha (1987)
Mathematische Zeitschrift
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Itokawa, Yoe (1993)
International Journal of Mathematics and Mathematical Sciences
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Yukio Otsu (1991)
Mathematische Zeitschrift
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Vladimir Rovenskiĭ (1998)
Annales Polonici Mathematici
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Submanifolds and foliations with restrictions on q-Ricci curvature are studied. In §1 we estimate the distance between two compact submanifolds in a space of positive q-Ricci curvature, and give applications to special classes of submanifolds and foliations: k-saddle, totally geodesic, with nonpositive extrinsic q-Ricci curvature. In §2 we generalize a lemma by T. Otsuki on asymptotic vectors of a bilinear form and then estimate from below the radius of an immersed submanifold in a simply...
Zhongmin Shen (1992)
Mathematische Zeitschrift
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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...
W. Roter (1977)
Colloquium Mathematicae
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Li Haizhong (1993)
Publications de l'Institut Mathématique
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Chen, Bang-Yen (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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