In a series of papers [4], [5], [6], [7] Cartan made an attempt to stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600" . He did not succeed, and, in fact, Cartan’s fundamental formula does not provide sufficient information to determine the possible number of distinct principal curvatures.Only later Munzner proved, using methods from algebraic topology,that the number g of distinct principal curvatures of an isoparametric hypersurface in equals 1, 2, 3, 4 or 6 . Cartan o:ole="" type="#_x0000_t75" , named as cartan hypersurface , corresponds with the homogeneou space. The isoparametric hypersurface change to cartan hypersurface if and only if it has 0 , and principal curvature. Chen introduced the immersed submanifolds in with the condition of coinciding to cartan hypersurface and infact he exhibited the new