We use the tangential component $ \psi ^{T} $ of an immersion of a compact hypersurface of the Euclidean space $ \mathbf{E}^{m+1} $ in finding two characterizations of a sphere. In first characterization, we use $ \psi ^{T} $ as a geodesic vector field (vector field with all its trajectories geodesics) and in the second characterization, we use $ \psi ^{T} $ to annihilate the de-Rham Laplace operator on the hypersurface.
Citation: Sharief Deshmukh, Mohammed Guediri. Characterizations of Euclidean spheres[J]. AIMS Mathematics, 2021, 6(7): 7733-7740. doi: 10.3934/math.2021449
We use the tangential component $ \psi ^{T} $ of an immersion of a compact hypersurface of the Euclidean space $ \mathbf{E}^{m+1} $ in finding two characterizations of a sphere. In first characterization, we use $ \psi ^{T} $ as a geodesic vector field (vector field with all its trajectories geodesics) and in the second characterization, we use $ \psi ^{T} $ to annihilate the de-Rham Laplace operator on the hypersurface.
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Sharief Deshmukh, Mohammed Guediri. Characterizations of Euclidean spheres[J]. AIMS Mathematics, 2021, 6(7): 7733-7740. doi: 10.3934/math.2021449
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