We shall provide a characterization of all isoparametric hypersurfaces $M$'s in a real space form $\tilde{M}(c)$ by observing the extrinsic Wshape of geodesics of $M$ in the ambient manifold $\tilde{M}(c)$.

MSC Classifications:

53C35, 53C20, 53C22 show english descriptions Symmetric spaces [See also 32M15, 57T15]
Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Geodesics [See also 58E10] 53C35 - Symmetric spaces [See also 32M15, 57T15]
53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]
53C22 - Geodesics [See also 58E10]

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