Lightlike Osserman submanifolds of semi-Riemannian manifolds

Details Lightlike Osserman submanifolds of semi-Riemannian manifolds Lightlike Osserman submanifolds of semi-Riemannian manifolds

2010-06-07

arxiv.org/abs/1006.1329v1

Mathematics

Differential Geometry

20 pages

Scientific paper

In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We introduce the notion of lightlike Osserman submanifolds and an example of 2-degenerate Osserman metric is given. Finally we give some results of symmetry properties on lightlike hy- persurfaces from Osserman condition.

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