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\(L^p\)-vanishing results for conformally flat manifolds and submanifolds. (English) Zbl 1280.53039

Summary: In this paper, we first obtain an \(L^p\)-vanishing result for solutions of Simons type equations under spectral assumptions on the relevant Schrödinger operators, and then get some applications to locally conformally flat Riemannian manifolds with constant nonnegative scalar curvature. Furthermore, we get some \(L^p\)-vanishing results for submanifolds.

MSC:

53C20 Global Riemannian geometry, including pinching
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C40 Global submanifolds
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