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In this paper, we deal with $n$ -dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space $L_{p}^{n + p}$ of index $p > 1$ , which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric...

Ricci and Casorati principal directions of $δ (2)$ Chen ideal submanifolds

Simona Decu, Anica Pantić, Miroslava Petrović-Torgašev, Leopold Verstraelen (2013)

Kragujevac Journal of Mathematics

Ricci curvature of real hypersurfaces in complex hyperbolic space

Bang-Yen Chen (2002)

Archivum Mathematicum

First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.

Riemannsche Mannigfaltigkeiten konstanter positiver Krümmung in euklidischen Räumen der Kodimension 2.

Wolfgang HENKE (1971)

Mathematische Annalen

Rigidity of minimal hypersurfaces of spheres with constant Ricci curvature.

Perdomo, Oscar (2004)

Revista Colombiana de Matemáticas

Rigidity of Minimal Submanifolds in Space Forms.

J.L.M. Barbosa, M. Dajczer, L.P. Jörge (1984)

Mathematische Annalen

Rigidity of Minimal Surfaces in S3.

Jayakumar Ramanathan (1988)

Manuscripta mathematica

Rigidity of Rank-One Factors of Compact Symmetric Spaces

Andrew Clarke (2011)

Annales de l’institut Fourier

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

Rigidity of the Clifford Tori in S3.

Yoshihisa Kitagawa (1988)

Mathematische Zeitschrift

S1-equivariant Minimal Tori in S4 and S1-equivariant Willmore Tori in S3.

Dirk FERUS, Franz Pedit (1990)

Mathematische Zeitschrift

Saddle surfaces admitting local support planes.

J.F. Voloch, D. Koutroufiotis (1985)

Journal für die reine und angewandte Mathematik

Scalar Curvature and Real Submanifolds of Codimension 2 of a Complex Projective Space.

Masafumi Okumura (1986)

Mathematische Zeitschrift

Screen conformal half-lightlike submanifolds.

Duggal, K.L., Sahin, B. (2004)

International Journal of Mathematics and Mathematical Sciences

Second variation and stabilities of minimal lagrangian submanifolds in Kähler manifolds.

Yong-Geun Oh (1990)

Inventiones mathematicae

Sectional curvatures of minimal hypersurfaces immersed in $S^{2 n + 1}$

He Kim, Seong Ahn, Masahiro Kon (1994)

Colloquium Mathematicae

Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds

Ülo Lumiste (2003)

Czechoslovak Mathematical Journal

A Riemannian manifold is said to be semisymmetric if $R (X, Y) \cdot R = 0$ . A submanifold of Euclidean space which satisfies $\bar{R} (X, Y) \cdot h = 0$ is called semiparallel. It is known that semiparallel submanifolds are intrinsically semisymmetric. But can every semisymmetric manifold be immersed isometrically as a semiparallel submanifold? This problem has been solved up to now only for the dimension 2, when the answer is affirmative for the positive Gaussian curvature. Among semisymmetric manifolds a special role is played by the foliated...

Semi-slant Riemannian maps into almost Hermitian manifolds

Kwang-Soon Park, Bayram Şahin (2014)

Czechoslovak Mathematical Journal

We introduce semi-slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of semi-slant immersions, invariant Riemannian maps, anti-invariant Riemannian maps and slant Riemannian maps. We obtain characterizations, investigate the harmonicity of such maps and find necessary and sufficient conditions for semi-slant Riemannian maps to be totally geodesic. Then we relate the notion of semi-slant Riemannian maps to the notion of pseudo-horizontally weakly conformal...

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