
A codimension \(2\) submanifold \(M\) of a pseudo-Riemannian manifold \((\bar M, \bar g)\) is called half light-like if the radical distribution \(\mathrm{Rad}(TM)=TM \cap TM ^{\perp}\) is a vector subbundle of \(TM\) and \(TM^\perp\) has rank one. Because of possible ranks of \(\mathrm{Rad}(TM)\), all codimension \(2\) light-like submanifolds are either half light-like or coisotropic. Given a half light-like submanifold \(M\) of \((\bar M,\bar g)\), one has \[ T\bar M = TM \oplus \mathrm{tr}(TM)=\mathrm{Rad}(TM) \oplus \mathrm{tr}(TM)\oplus _{\mathrm{orth}} S(TM), \] where \(\mathrm{tr}(TM)\) and \( S(TM)\) respectively denote the transversal vector bundle and the screen distribution and \(\oplus _{\mathrm{orth}}\) denotes the \(\bar g\)-orthogonal direct sum. In the paper under review, the authors consider half light-like submanifolds of indefinite Kenmotsu manifolds \((\bar M, J,\zeta,\theta,\bar g)\). The following results are proved: \(\bullet\) The structure \(1\)-form \(\theta\) is closed on \(M\). \(\bullet\) If \(M\) is locally symmetric and \(tr(TM)\) is parallel (with respect to \(\bar \nabla\)), then the induced Ricci type tensor \(R^{(0,2)}\) of \(M\) is symmetric. \(\bullet\) If \(M\) is irrotational and locally symmetric and \(tr(TM)\) is parallel, then \(M\) has constant sectional curvature \(0\) and \(\zeta\) is normal to \(M\).
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), irrotational submanifolds, Global submanifolds, local symmetry, half light-like submanifolds, indefinite Kenmotsu manifolds
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), irrotational submanifolds, Global submanifolds, local symmetry, half light-like submanifolds, indefinite Kenmotsu manifolds
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