Article Dans Une Revue Symmetry, Integrability and Geometry : Methods and Applications Année : 2023

A Poincaré formula for differential forms and applications

Résumé

We prove a new general Poincar\'e-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its limiting case in codimension one. A new Ros-type inequality for differential forms is also derived assuming the existence of a nonzero parallel form on the manifold.

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hal-04155972 , version 1 (07-07-2023)

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Nicolas Ginoux, Georges Habib, Simon Raulot. A Poincaré formula for differential forms and applications. Symmetry, Integrability and Geometry : Methods and Applications, 2023, 19 (88), 17 p. ⟨10.3842/SIGMA.2023.088⟩. ⟨hal-04155972⟩
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