Screen conformal half-lightlike submanifolds.
Duggal, K.L., Sahin, B. (2004)
International Journal of Mathematics and Mathematical Sciences
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Duggal, K.L., Sahin, B. (2004)
International Journal of Mathematics and Mathematical Sciences
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Chen, Bang-Yen (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Oprea, Teodor (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Pitiş, Gheorghe (2005)
The New York Journal of Mathematics [electronic only]
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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.
Olteanu, Andreea (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Decu, Simona, Haesen, Stefan, Verstraelen, Leopold (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Ryszard Deszcz, Stanisław Ewert-Krzemieniewski, Jerzy Policht (1988)
Colloquium Mathematicae
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Yoon, Dae Won (2005)
International Journal of Mathematics and Mathematical Sciences
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Andrzej Derdzinski (2012)
Open Mathematics
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The connected components of the zero set of any conformal vector field v, in a pseudo-Riemannian manifold (M, g) of arbitrary signature, are of two types, which may be called ‘essential’ and ‘nonessential’. The former consist of points at which v is essential, that is, cannot be turned into a Killing field by a local conformal change of the metric. In a component of the latter type, points at which v is nonessential form a relatively-open dense subset that is at the same time a totally...
Mihai, Ion, Rosca, Radu, Ghişoiu, Valentin (2005)
International Journal of Mathematics and Mathematical Sciences
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Branson, Thomas
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The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.