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Zbl 1158.53045
Şahin, Bayram
Slant lightlike submanifolds of indefinite Hermitian manifolds. (English)
[J] Balkan J. Geom. Appl. 13, No. 1, 107-119 (2008). ISSN 1224-2780

Let $(M,g,J)$ be an almost Hermitian manifold. A submanifold $N$ of $(M,g,J)$ is called slant if for each $p\in N$ and $X\in T\sb pN$ the angle $\theta$ between $JX$ and $T\sb pN$ is constant [{\it B.-Y. Chen}, Bull. Aust. Math. Soc. 41, No. 1, 135--147 (1990; Zbl 0677.53060)]. Special cases of slant submanifolds are almost complex ($\theta=0$) and totally real ($\theta=\pi/2$) submanifolds. Let $M\sp n$ be a submanifold immersed in a semi-Riemannian manifold $(M\sp{n+k},g)$. The distribution $\text{Rad}\,(TM)=TM\cap TM\sp\perp$ is called the radical and its complementary distribution $S(TM)$ is called the screen distribution. A submanifold $M\sp n$ is called a light-like submanifold if $\text{Rad}\,(TM)$ is of rank $k$ [{\it K. L. Duggal} and {\it A. Bejancu} Lightlike submanifolds of semi-Riemannian manifolds and applications (Mathematics and its Applications Dordrecht: Kluwer Academic Publishers) (1996; Zbl 0848.53001)]. The goal of this paper is to introduce the notion of a slant light-like submanifold of an indefinite Hermitian manifold $(M,g,J)$. The author proves a characterization theorem for the existence of slant light-like submanifolds and shows that co-isotropic $CR$-light-like submanifolds are slant light-like submanifolds. Also, minimal slant light-like submanifolds are presented and some examples and two characterization theorems are given.
[Andrew Bucki (Edmond)]

MSC 2000:: *53C40 Submanifolds (differential geometry)
53C15 Geometric structures on manifolds
53C50 Lorentz manifolds, manifolds with indefinite metrics

Keywords: degenerate metric; slant lightlike submanifold; Hermitian manifold

Citations: Zbl 0677.53060; Zbl 0848.53001

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