Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

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.

Homogeneous hessian manifolds

Hirohiko Shima — 1980

Annales de l'institut Fourier

A flat affine manifold is said to Hessian if it is endowed with a Riemannian metric whose local expression has the form g i j = 2 Φ x i x j where Φ is a C -function and { x 1 , ... , x n } is an affine local coordinate system. Let M be a Hessian manifold. We show that if M is homogeneous, the universal covering manifold of M is a convex domain in R n and admits a uniquely determined fibering, whose base space is a homogeneous convex domain not containing any full straight line, and whose fiber is an affine subspace of R n .

Page 1

Download Results (CSV)