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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-parallel Lightlike Hypersurfaces of Indefinite Cosymplectic Space Forms

Abhitosh Upadhyay, Ram Shankar Gupta (2011)

Publications de l'Institut Mathématique

Semi-riemannian Manifolds Whose Weyl Tensor is a Kulkarni--nomizu Square

Malgorzata Glogowska (2002)

Publications de l'Institut Mathématique

Semi-Riemannian manifolds whose Weyl tensor is a Kulkarni-Nomizu square.

Głogowska, Małgorzata (2002)

Publications de l'Institut Mathématique. Nouvelle Série

Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces

Marta Dabrowska, Filip Defever, Ryszard Deszcz, Dorota Kowalczyk (2000)

Publications de l'Institut Mathématique

Shape Operators and Structure Tensors of Real Hypersurfaces in Nonflat Quaternionic Space Forms

Sadahiro Maeda, Toshiaki Adachi (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms in terms of their shape operators and structure tensors.

Singular Klein manifolds.

Abdel-All, N.H. (1995)

Portugaliae Mathematica

Singular points of lightlike hypersurfaces of the de Sitter space.

Akivis, M.A., Goldberg, V.V. (1998)

Publications de l'Institut Mathématique. Nouvelle Série

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Constantin Călin, Mircea Crasmareanu (2014)

Czechoslovak Mathematical Journal

We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly...

In this paper we review some of the concepts and results of V. I. Arnol’d [1] for curves in $S^{2}$ and extend them to curves and surfaces in $S^{3}$ .

Some results on warped product submanifolds of a Sasakian manifold.

Uddin, Siraj, Khan, V.A., Khan, Huzoor H. (2010)

International Journal of Mathematics and Mathematical Sciences

Some theorems on austere submanifolds.

Suceavă, Bogdan (1997)

Balkan Journal of Geometry and its Applications (BJGA)

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Displaying 1 – 20 of 38

Scalar curvature on lightlike hypersurfaces.

Screen conformal half-lightlike submanifolds.

Screen transversal lightlike submanifolds of indefinite cosymplectic manifolds

Semi-invariant submanifolds of a Lorentzian para-Sasakian manifold.

Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds

Semi-parallel Lightlike Hypersurfaces of Indefinite Cosymplectic Space Forms

Semi-riemannian Manifolds Whose Weyl Tensor is a Kulkarni--nomizu Square

Semi-Riemannian manifolds whose Weyl tensor is a Kulkarni-Nomizu square.

Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces

Shape Operators and Structure Tensors of Real Hypersurfaces in Nonflat Quaternionic Space Forms

Singular Klein manifolds.

Singular points of lightlike hypersurfaces of the de Sitter space.

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

Slant surfaces with prescribed Gaussian curvature.

Some characterizations of 2-symmetric submanifolds in spaces of constant curvature

Some curvature conditions of the type 2x4 on the submanifolds satisfying Chen's equality

Some remarks on duality in $S^{3}$

Some results on warped product submanifolds of a Sasakian manifold.

Some theorems on austere submanifolds.

Currently displaying 1 – 20 of 38