Simons-Type Inequality on a New Class of Willmore-Type Hypersurfaces in Spheres
In the paper,we define a class of functionals Tn of hypersurfaces in general dimensional spheres as generation of Willmore functionals.We will prove that Tn have similar properties as Willmore functionals,that is to say,Tn are always conformal invariants,when n is even,the Tn-critical closed hypersurfaces also satisfy Simons-type inequalities,which shows that Tn-critical closed hypersurfaces have sort of rigidity in geometry.
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