Weakly-Einstein hermitian surfaces

Vestislav Apostolov; Oleg Muškarov

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 5, page 1673-1692
  • ISSN: 0373-0956

Abstract

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A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as * -Einstein condition we obtain a complete classification of the compact locally homogeneous * -Einstein Hermitian surfaces. We also provide large families of non-homogeneous * -Einstein (but non-Einstein) Hermitian metrics on ℂ ℙ 2 ♯ ℂ ℙ ‾ 2 , ℂ ℙ 1 × ℂ ℙ 1 , and on the product surface X × Y of two curves X and Y whose genuses are greater than 1 and 0, respectively.

How to cite

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Apostolov, Vestislav, and Muškarov, Oleg. "Weakly-Einstein hermitian surfaces." Annales de l'institut Fourier 49.5 (1999): 1673-1692. <http://eudml.org/doc/75398>.

@article{Apostolov1999,
abstract = {A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as $*$-Einstein condition we obtain a complete classification of the compact locally homogeneous $*$-Einstein Hermitian surfaces. We also provide large families of non-homogeneous $*$-Einstein (but non-Einstein) Hermitian metrics on $\{\Bbb C\}\{\Bbb P\}^2\sharp \bar\{\{\Bbb C\}\{\Bbb P\}\}^2$, $\{\Bbb C\}\{\Bbb P\}^1\times \{\Bbb C\}\{\Bbb P\}^1$, and on the product surface $X\times Y$ of two curves $X$ and $Y$ whose genuses are greater than 1 and 0, respectively.},
author = {Apostolov, Vestislav, Muškarov, Oleg},
journal = {Annales de l'institut Fourier},
keywords = {Hermitian surface; Einstein metric; locally conformally Kähler surface; Hopf surface; *-Einstein; Einstein; Vaisman metric},
language = {eng},
number = {5},
pages = {1673-1692},
publisher = {Association des Annales de l'Institut Fourier},
title = {Weakly-Einstein hermitian surfaces},
url = {http://eudml.org/doc/75398},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Apostolov, Vestislav
AU - Muškarov, Oleg
TI - Weakly-Einstein hermitian surfaces
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 5
SP - 1673
EP - 1692
AB - A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as $*$-Einstein condition we obtain a complete classification of the compact locally homogeneous $*$-Einstein Hermitian surfaces. We also provide large families of non-homogeneous $*$-Einstein (but non-Einstein) Hermitian metrics on ${\Bbb C}{\Bbb P}^2\sharp \bar{{\Bbb C}{\Bbb P}}^2$, ${\Bbb C}{\Bbb P}^1\times {\Bbb C}{\Bbb P}^1$, and on the product surface $X\times Y$ of two curves $X$ and $Y$ whose genuses are greater than 1 and 0, respectively.
LA - eng
KW - Hermitian surface; Einstein metric; locally conformally Kähler surface; Hopf surface; *-Einstein; Einstein; Vaisman metric
UR - http://eudml.org/doc/75398
ER -

References

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