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Unit vector fields on antipodally punctured spheres: big index, big volume

Fabiano G. B. Brito, Pablo M. Chacón, David L. Johnson (2008)

Bulletin de la Société Mathématique de France

We establish in this paper a lower bound for the volume of a unit vector field v defined on 𝐒 n { ± x } , n = 2 , 3 . This lower bound is related to the sum of the absolute values of the indices of v at x and - x .

[unknown]

Thomas Morzadec (0)

Annales de l’institut Fourier

[unknown]

Raimundo Araújo dos Santos, Maria A.B. Hohlenwerger, Osamu Saeki, Taciana O. Souza (0)

Annales de l’institut Fourier

Vanishing theorems for compact hessian manifolds

Hirohiko Shima (1986)

Annales de l'institut Fourier

A manifold is said to be Hessian if it admits a flat affine connection D and a Riemannian metric g such that g = D 2 u where u is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.

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