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Rigidity of noncompact manifolds with cyclic parallel Ricci curvature

Yi Hua Deng (2014)

Annales Polonici Mathematici

We prove that if M is a complete noncompact Riemannian manifold whose Ricci tensor is cyclic parallel and whose scalar curvature is nonpositive, then M is Einstein, provided the Sobolev constant is positive and an integral inequality is satisfied.

Rigidity of Rank-One Factors of Compact Symmetric Spaces

Andrew Clarke (2011)

Annales de l’institut Fourier

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

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