
doi: 10.4064/ap100-2-4
The authors define totally umbilical submanifolds of Finsler manifolds using the second fundamental form introduced by Q. He and Y. B. Shen. They study totally umbilical submanifolds of Finsler manifolds establishing some simpler equations related to curvatures of Finsler submanifolds and the curvatures of the ambient space. They obtain some relations between totally umbilical submanifolds of a Randers space \((\widetilde{M},\widetilde{\alpha}+\widetilde{\beta})\) and of the Riemannian manifold \((\widetilde{M},\widetilde{\alpha})\) and prove a rigidity theorem for complete and connected totally umbilical submanifolds of a special Randers space. Finally, they give an example of a totally umbilical submanifold of a Randers space.
Global differential geometry of Finsler spaces and generalizations (areal metrics), second fundamental form, minimal submanifold, Global submanifolds, totally umbilical submanifold, Randers space
Global differential geometry of Finsler spaces and generalizations (areal metrics), second fundamental form, minimal submanifold, Global submanifolds, totally umbilical submanifold, Randers space
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