Vanishing theorems for compact hessian manifolds
Annales de l'Institut Fourier, Volume 36 (1986) no. 3, p. 183-205

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.

Une variété est dite hessienne si elle admet une connexion plate D et une métrique riemannienne g telle que g=D 2 uu est une fonction locale. On étudie la cohomologie des variétés hessiennes et on montre un théorème de dualité et des “vanishing theorems”.

@article{AIF_1986__36_3_183_0,
     author = {Shima, Hirohiko},
     title = {Vanishing theorems for compact hessian manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {36},
     number = {3},
     year = {1986},
     pages = {183-205},
     doi = {10.5802/aif.1065},
     zbl = {0586.57013},
     mrnumber = {88f:53059},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1986__36_3_183_0}
}
Shima, Hirohiko. Vanishing theorems for compact hessian manifolds. Annales de l'Institut Fourier, Volume 36 (1986) no. 3, pp. 183-205. doi : 10.5802/aif.1065. http://www.numdam.org/item/AIF_1986__36_3_183_0/

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