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Displaying similar documents to “Screen conformal half-lightlike submanifolds.”

On canonical screen for lightlike submanifolds of codimension two

K. Duggal (2007)

Open Mathematics

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In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.

Conformal nullity of isotropic 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.

Totally umbilical submanifolds in some semi-Riemannian manifolds

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.