Rectifying submanifold; Rectifying subspace; Pseudo-Euclidean space; Concurrent vector field; Space-like submanifold; Position vector field.
The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds in an arbitrary pseudo-Euclidean space with codimension greater than one.
International Electronic Journal of Geometry
Chan, Bang Yen and Oh, Yun Myung, "Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces" (2017). Faculty Publications. 709.
Retrieved August 24, 2018 from http://dergipark.gov.tr/download/article-file/355632