Abstract
In 2000, Bejancu–Farran introduced the class of generalized Landsberg manifolds which contains the class of Landsberg manifolds. In this paper, 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 \(\mathbf{H}=0\).
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Acknowledgments
The author would like to thank Professor Hassan Akbar-Zadeh for his valuable comments. Also, I would like to thank the referees for their careful reading of the manuscript and helpful suggestions.
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Tayebi, A. On the class of generalized Landsberg manifolds. Period Math Hung 72, 29–36 (2016). https://doi.org/10.1007/s10998-015-0108-x
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DOI: https://doi.org/10.1007/s10998-015-0108-x