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- W745267474 abstract "Abstract. We introduce three classes of quaternion lightlike submani-folds, screen real lightlike submanifolds and CR lightlike submanifolds ofan inde nite quaternion Kaehlerian manifold and study the geometry ofleaves of their distributions. 1. IntroductionIt is well known that on an inde nite quaternion Kaehlerian manifold Mwith an inde nite Riemannian metric g there exists a 3-dimensional vectorbundle V of tensors of type (1;1) with local cross section of almost Hermitianstructures f ; = 1;2;3gsatisfying certain conditions(cf. [7]). In case Misnondegenerate submanifold in an inde nite quaternion Kaehlerian manifold M,the theory of quaternion CR submanifolds of quaternion Kaehlerian manifoldswas introduced in [1]. In case of lightlike(or degenerate) submanifold M ofinde nite quaternion Kaehlerian manifold M, several vector bundles involved,for example, Rad(TM);S(TM);ltr(TM) and S(TM ? ), etc. (see section 2).Therefore there would be several classes of lightlike submanifolds according tothe action of almost Hermitian structures f ; = 1;2;3gon subbundles of thetangent bundle TM. In this article we introduce the general notion of quater-nion CR lightlike submanifolds, which is similar to the concept of lightlike CRsubmanifolds of inde nite Kaehler manifolds([4]). We study the integrabilityconditions of their distributions, and investigate the geometry of leaves of thedistributions involved in the induced quaternion CR structure on M:Contraryto the nondegenerate case, but similar to the lightlike CR submanifolds of in-de nite Kaehler manifolds, they do not include the quaternion lightlike and thescreen real lightlike submanifolds." @default.
- W745267474 created "2016-06-24" @default.
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- W745267474 date "2009-01-01" @default.
- W745267474 modified "2023-09-23" @default.
- W745267474 title "LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE QUATERNION KAEHLERIAN MANIFOLD" @default.
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