Skip to main content Accessibility help
×
Home

HOMOGENEOUS SASAKI AND VAISMAN MANIFOLDS OF UNIMODULAR LIE GROUPS

  • D. ALEKSEEVSKY (a1), K. HASEGAWA (a2) and Y. KAMISHIMA (a3)

Abstract

A Vaisman manifold is a special kind of locally conformally Kähler manifold, which is closely related to a Sasaki manifold. In this paper, we show a basic structure theorem of simply connected homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups, up to holomorphic isometry. For the case of unimodular Lie groups, we obtain a complete classification of simply connected Sasaki and Vaisman unimodular Lie groups, up to modification.

Copyright

References

Hide All
[1] Alekseevsky, D., Cortés, V., Hasegawa, K. and Kamishima, Y., Homogeneous locally conformally Kähler and Sasaki manifolds , Internat. J. Math. 26(06) (2015), 129.
[2] Boothby, W. M. and Wang, H. C., On contact manifolds , Ann. of Math. (2) 68(3) (1958), 721734.
[3] Borel, A., Kählerian coset spaces of semi-simple Lie groups , Proc. Natl Acad. Sci. USA 40 (1954), 721734.
[4] Boyer, C. P. and Galicki, K., Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2008.
[5] Dorfmeister, J. and Nakajima, K., The fundamental conjecture for homogeneous Kähler manifolds , Acta. Math. 161 (1988), 2370.
[6] Grauert, H., Analytische Faserungen über holomorph-vollständigen Räumen , Math. Ann. 135 (1958), 263273.
[7] Hano, J., On Kählerian homogeneous spaces of unimodular Lie groups , Amer. J. Math. 79 (1957), 885900.
[8] Hasegawa, K. and Kamishima, Y., Locally conformally Kähler structures on homogeneous spaces , Progr. Math. 308 (2015), 353372.
[9] Hasegawa, K. and Kamishima, Y., Compact homogeneous locally conformally Kähler manifolds , Osaka J. Math. 53 (2016), 683703.
[10] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry II, Wiley Classics Library, John Wiley & Sons, New York, 1996.
[11] Koszul, J. K., Sur la forme hermitienne canonique des espaces homogènes complexes , Canad. J. Math. 7 (1955), 562576.
[12] Nakajima, K., Homogeneous Kähler manifolds of non-degenerate Ricci curvature , J. Math. Soc. Japan 42 (1990), 475494.
[13] Sawai, H., Locally conformal Kähler structures on compact nilmanifolds with left-invariant complex structures , Geom. Dedicata 125 (2007), 93101.
[14] Sawai, H., Structure theorem for Vaisman completely solvable solvmanifolds , J. Geom. Phys. 114 (2017), 581586.
[15] Vinberg, E. B., Gindikin, S. G. and Piatetskii-Shapiro, I. I., Classification and canonical realization of complex homogeneous domains , Trans. Moscow Math. Soc. 12 (1963), 404437.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

HOMOGENEOUS SASAKI AND VAISMAN MANIFOLDS OF UNIMODULAR LIE GROUPS

  • D. ALEKSEEVSKY (a1), K. HASEGAWA (a2) and Y. KAMISHIMA (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed