On the index of stability of (r, s)-linear Weingarten Clifford tori
DOI:
https://doi.org/10.17268/sel.mat.2023.01.10Keywords:
Unit Euclidean sphere, higher order mean curvatures, (r, s)-linear Weingarten Clifford torus, Jacobi operator, index of (r, s)-stabilityAbstract
For entire numbers r and s satisfying 0 ≤ r ≤ s ≤ n − 2, we showed that the index of (r, s)-stability of a (r, s)-linear Weingarten Clifford torus immersed into the (n + 1)-dimensional unit Euclidean sphere, that has a linear combination of their higher order mean curvatures Hr+1 and Hs+1 being null, is exactly equal to n + 3 provided that a geometric condition involving Hr+2 and Hs+2 is satisfied.
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