Chi Hin Chan, Magdalena Czubak
Published 2022-12-22Version 1
We extend the Gauss formula relating the extrinsic connection to the intrinsic connection to a formula for the extrinsic, Euclidean Laplacian to the intrinsic Laplacian of a vector field on a hypersurface. As a byproduct, we derive a formula for the Laplacian of a $1$-form on a surface of revolution in terms of the Lie derivatives. Physically, these formulas are motivated by the study of the formulation of the incompressible Navier-Stokes equations on a Riemannian manifold.
The $Q$-curvature on a 4-dimensional Riemannian manifold $(M,g)$ with $\int_MQdV_g=8π^2$
Small surfaces of Willmore type in Riemannian manifolds
Convexity of $λ$-hypersurfaces
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