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Mathematical analysis demonstrates vanishing homology conditions in Euclidean CR-warped product submanifolds, establishing that these geometric structures are homotopy spheres.
We obtain a necessary condition for homology group to be zero on CR-warped product submanifold in Euclidean spaces in terms of second fundamental form of the submanifold and warping function. By using this condition, we show that such CR-warped product submanifold is a homotopy sphere.
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Fulya Şahin (2017) studied this question.
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