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Gilkey, P.B. (2002) Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor. World Scientific, Singapore.
https://doi.org/10.1142/9789812799692

has been cited by the following article:

• TITLE: Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds

  AUTHORS: Domitien Ndayirukiye, Gilbert Nibaruta, Ménédore Karimumuryango, Aboubacar Nibirantiza

  KEYWORDS: Lightlike (Sub)Manifolds, Algebraic Curvature Tensor, Total Umbilicity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.12, December 19, 2019

  ABSTRACT: Lightlike warped product manifolds are considered in this paper. The geometry of lightlike submanifolds is difficult to study since the normal vector bundle intersects with the tangent bundle. Due to the degenerate metric, the induced connection is not metric and it follows that the Riemannian curvature tensor is not algebraic. In this situation, some basic techniques of calulus are not useable. In this paper, we consider lightlike warped product as submanifold of semi-Riemannian manifold and establish some remarkable geometric properties from which we establish some conditions on the algebraicity of the induced Riemannian curvature tensor.