On the Focal Locus of a Submanifold in a Riemannian Manifold of Constant Sectional Curvature
Hukum Singh (1985)
Publications de l'Institut Mathématique
Similarity:
Hukum Singh (1985)
Publications de l'Institut Mathématique
Similarity:
Trenčevski, K. (1999)
Novi Sad Journal of Mathematics
Similarity:
Ziqi Sun (2003)
Colloquium Mathematicae
Similarity:
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...
Vladimir Rovenskiĭ (1998)
Annales Polonici Mathematici
Similarity:
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...
Chen, Bang-Yen (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Similarity:
Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar (2016)
Annales Polonici Mathematici
Similarity:
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...
Franki Dillen, Johan Fastenakels (2009)
Open Mathematics
Similarity:
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.
Simona Decu, Anica Pantić, Miroslava Petrović-Torgašev, Leopold Verstraelen (2013)
Kragujevac Journal of Mathematics
Similarity:
Gupta, Ram Shankar, Haider, S.M.Khrusheed, Sharfuddin, A. (2006)
Balkan Journal of Geometry and its Applications (BJGA)
Similarity:
Arslan, Kadri, Ezentas, Ridvan, Mihai, Ion, Murathan, Cengizhan, Özgür, Cihan (2002)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Ryszard Deszcz, Miroslava Petrović-Torgašev, Zerrin Şentürk, Leopold Verstraelen (2010)
Publications de l'Institut Mathématique
Similarity:
Decu, Simona, Haesen, Stefan, Verstraelen, Leopold (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Similarity: