Abstract
Generic lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection
Highlights
A lightlike submanifold M of an indefinite almost complex manifold M, with an indefinite almost complex structure J, is called generic lightlike submanifold if there exists a screen distribution S(T M ) of M such thatJ(S(T M )⊥) ⊂ S(T M ), (1)where S(T M )⊥ is the orthogonal complement of S(T M ) in the tangent bundle T M of M, i. e., T M = S(T M ) ⊕orth S(T M )⊥
Where θ is a 1-form on M associated with a smooth unit vector field ζ by θ(X) = g(X, ζ)
We denote by X, Y and Zthe smooth vector fields on M
Summary
The object of present study is generic lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We characterize generic lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection. A generic lightlike submanifold M of an indefinite Kaehler manifold M is called recurrent if it admits a recurrent structure tensor field F .
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