labs.tex

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In $2000$, Bejancu-Farran introduced the class of generalized Landsberg  manifolds which contains the class of Landsberg manifolds. In this thesis, we prove three global results for generalized Landsberg manifolds. First, we show that every compact generalized Landsberg manifold is a Landsberg manifold. Then we prove that every complete generalized landsberg manifold with relatively isotropic landsberg curvature reduces to a Landsberg manifold. Finally, we show that every generalized Landsberg manifold with vanishing Douglas curvature satisfies $ H=0 $.