Hessian manifolds of constant Hessian sectional curvature

Hirohiko SHIMA

doi:10.2969/jmsj/04740735

Hirohiko SHIMA

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 4 Pages 735-753

DOI https://doi.org/10.2969/jmsj/04740735

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Published: 1995 Received: January 14, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Amari, Differential-Geometric Methods in Statistics, Lecture Notes in Statist., 28, Springer, 1985.
2) C. Atkinson and A. F. Mitchell, Rao's distance measure, Sankhya Ser. A, 43 (1981), 345-365.
3) R. Bott and S. S. Chern, Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections, Acta Math., 114 (1965), 71-112.
4) B. Y. Chen and K. Ogiue, Some characterizations of complex space forms in terms of Chern classes, Quart. J. Math. Oxford, 26 (1975), 459-464.
5) H. Shima, Homogeneous Hessian manifolds, Ann. Inst. Fourier (Grenoble), 30-3 (1980), 91-128.
6) H. Shima, Vanishing theorems for compact Hessian manifolds, Ann. Inst. Fourier (Grenoble), 36-3 (1986), 183-205.
7) H. Shima, Hessian manifolds, Séminaire Gaston Darboux de géométrie et topologie différentielle, Université Montpellier, (1988-1989), pp. 1-48.
8) H. Shima and K. Yagi, Geometry of compact Hessian manifolds, preprint.
9) L. T. Skovgaard, A Riemannian geometry of the multivariate normal model, Scand. J. Statist., 11 (1984), 211-223.
10) K. Yagi, Convexity of a Hessian manifold, Studia Humana et Natumalia, Faculty of Liberal Studies, Kyoto Prefectural University of Medicine, (1985), 1-2.

Right : [1] S. Amari, Differential-Geometric Methods in Statistics, Lecture Notes in Statist., 28, Springer, 1985.
[2] C. Atkinson and A. F. Mitchell, Rao's distance measure, Sankhya Ser. A, 43 (1981), 345-365.
[3] R. Bott and S. S. Chern, Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections, Acta Math., 114 (1965), 71-112.
[4] B. Y. Chen and K. Ogiue, Some characterizations of complex space forms in terms of Chern classes, Quart. J. Math. Oxford, 26 (1975), 459-464.
[5] H. Shima, Homogeneous Hessian manifolds, Ann. Inst. Fourier (Grenoble), 30-3 (1980), 91-128.
[6] H. Shima, Vanishing theorems for compact Hessian manifolds, Ann. Inst. Fourier (Grenoble), 36-3 (1986), 183-205.
[7] H. Shima, Hessian manifolds, Séminaire Gaston Darboux de géométrie et topologie différentielle, Université Montpellier, (1988-1989), pp. 1-48.
[8] H. Shima and K. Yagi, Geometry of compact Hessian manifolds, preprint.
[9] L. T. Skovgaard, A Riemannian geometry of the multivariate normal model, Scand. J. Statist., 11 (1984), 211-223.
[10] K. Yagi, Convexity of a Hessian manifold, Studia Humana et Natumalia, Faculty of Liberal Studies, Kyoto Prefectural University of Medicine, (1985), 1-2.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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