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Vanishing theorems for compact hessian manifolds

Hirohiko Shima

Annales de l'institut Fourier (1986)

  • Volume: 36, Issue: 3, page 183-205
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Shima, Hirohiko. "Vanishing theorems for compact hessian manifolds." Annales de l'institut Fourier 36.3 (1986): 183-205. <http://eudml.org/doc/74723>.

@article{Shima1986,
abstract = {A manifold is said to be Hessian if it admits a flat affine connection $D$ and a Riemannian metric $g$ such that $g=D^ 2u$ where $u$ is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.},
author = {Shima, Hirohiko},
journal = {Annales de l'institut Fourier},
keywords = {cohomology for Hessian manifolds; duality theorem; vanishing theorems},
language = {eng},
number = {3},
pages = {183-205},
publisher = {Association des Annales de l'Institut Fourier},
title = {Vanishing theorems for compact hessian manifolds},
url = {http://eudml.org/doc/74723},
volume = {36},
year = {1986},
}

TY - JOUR
AU - Shima, Hirohiko
TI - Vanishing theorems for compact hessian manifolds
JO - Annales de l'institut Fourier
PY - 1986
PB - Association des Annales de l'Institut Fourier
VL - 36
IS - 3
SP - 183
EP - 205
AB - A manifold is said to be Hessian if it admits a flat affine connection $D$ and a Riemannian metric $g$ such that $g=D^ 2u$ where $u$ is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.
LA - eng
KW - cohomology for Hessian manifolds; duality theorem; vanishing theorems
UR - http://eudml.org/doc/74723
ER -

References

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  3. [3] K. KODAIRA, On cohomology groups of compact analytic varieties with coefficients in some analytic faisceaux, Proc. Nat. Acad. Sci., U.S.A., 39 (1953), 865-868. Zbl0051.14502MR16,74b
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  8. [8] J. MORROW and K. KODAIRA, Complex manifolds, Holt, Rinehart and Winston, Inc., 1971. Zbl0325.32001MR46 #2080
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  10. [10] H. SHIMA, On certain locally flat homogeneous manifolds of solvable Lie groups, Osaka J. Math., 13 (1976), 213-229. Zbl0332.53032MR54 #1131
  11. [11] H. SHIMA, Symmetric spaces with invariant locally Hessian structures, J. Math. Soc. Japan, 29 (1977), 581-589. Zbl0349.53036MR56 #9462
  12. [12] H. SHIMA, Compact locally Hessian manifolds, Osaka J. Math., 15 (1978), 509-513. Zbl0415.53032MR80e:53054
  13. [13] H. SHIMA, Homogeneous Hessian manifolds, Ann. Inst. Fourier, Grenoble, 30-3 (1980), 91-128. Zbl0424.53023MR82a:53054
  14. [14] H. SHIMA, Hessian manifolds and convexity, in Manifolds, and Lie groups, Papers in honor of Y. Matsushima, Progress in Mathematics, vol. 14, Birkhäuser, Boston, Basel, Stuttgart, 1981, 385-392. Zbl0481.53038MR83h:53066
  15. [15] K. YAGI, On Hessian structures on an affine manifold, in Manifolds and Lie groups. Papers in honor of Y. Matsushima, Progress in Mathematics, vol. 14, Birkhäuser, Boston, Basel, Stuttgart, 1981, 449-459. Zbl0495.53011MR83h:53067

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