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On the Structure of the Cut Locus in Certain Classes of Warped Product Manifolds
In this paper, we determine the structure of the cut locus for a class of complete warped product manifolds $M=(R^1\times S^1,dt^2+m(t)^2dθ^2)$, where the warping function $m(t)$ is positive and even, under the assumption that there exists a positive number $t_1$ such that the Gaussian curvature is
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