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De Lellis-Topping type inequalities for f-Laplacians

Guangyue Huang, Fanqi Zeng (2016)

Studia Mathematica

We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.

De Rham decomposition theorems for foliated manifolds

Robert A. Blumenthal, James J. Hebda (1983)

Annales de l'institut Fourier

We prove that if M is a complete simply connected Riemannian manifold and F is a totally geodesic foliation of M with integrable normal bundle, then M is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.

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