Vanishing theorems for compact hessian manifolds

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1986 English Publisher:MathDoc/Centre MersenneJournal:Annales de l'Institut Fourier, volume 36, pages 183-205 (eissn: 1777-5310,

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Authors: Shima, Hirohiko;

doi: 10.5802/aif.1065

Vanishing theorems for compact hessian manifolds

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Abstract

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.

Keywords

cohomology for Hessian manifolds, Algebraic topology on manifolds and differential topology, Duality in algebraic topology, vanishing theorems, Global Riemannian geometry, including pinching, duality theorem

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