In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae...In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.展开更多
In this paper we investigate the Einstein＇s hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed an...In this paper we investigate the Einstein＇s hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein＇s hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.展开更多
The authors compute non-zero structure constants of the full flag manifold M = SO(7)/T with nine isotropy summands,then construct the Einstein equations.With the help of computer they get all the forty-eight positive ...The authors compute non-zero structure constants of the full flag manifold M = SO(7)/T with nine isotropy summands,then construct the Einstein equations.With the help of computer they get all the forty-eight positive solutions(up to a scale) for SO(7)/T,up to isometry there are only five G-invariant Einstein metrics,of which one is Khler Einstein metric and four are non-Khler Einstein metrics.展开更多
Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove...Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E’=E|<sub> \D</sub> compatible with the parabolic structure, whose curvature is square integrable.展开更多
In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some...In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some very special cases,the coset space G×G/△(K)carries at least two invariant Einstein metrics.Furthermore,in the case that G1,G2 and K are simple Lie groups,with K■G1,K■G2,and G_1≠G2,such that G_1/K and G2/K are compact isotropy irreducible spaces,we give a complete classification of invariant Einstein metrics on the coset space G1×G2/△(K).展开更多
Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l+ m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on ge...Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l+ m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there are infinitely many spaces of the type SO(k + l + m)/SO(k)× SO(l) × SO(m) admitting exactly two, three, or four invariant Einstein metrics up to a homothety.展开更多
The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-Khler metric on the special type ...The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-Khler metric on the special type of Hua domains is given and the sharp estimate of holomorphic sectional curvature under this metric is also obtained.In the meantime we also prove that the complete Einstein-Khler metric is equivalent to the Bergman metric on the special type of Hua domain.展开更多
We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein＇s prescription in general relativity. As required for the Einstein energy-momentu...We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein＇s prescription in general relativity. As required for the Einstein energy-momentum complex, we perform the calculations in quasi-Cartesian coordinates. We also calculate the momentum components and obtain a zero value, as expected from the geometry of the metric.展开更多
基金supported by NSFC (12071228,11901300, 51535008)Natural Science Research of Jiangsu Education Institutions of China (19KJB110015)。
文摘In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.
基金The project supported in part by the National Natural Science Foundation of China under Grant No. 10671124 and the Program for New Century Excellent Talents in University of China under Grant No. NCET-05-0390 Acknowledgments The author would like to thank the Center of Mathematical Sciences at Zhejiang University for the great support and hospitality and the referee for pertinent comments and valuable suggestions.
文摘In this paper we investigate the Einstein＇s hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein＇s hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.
基金supported by the National Natural Science Foundation of China(Nos.11501390,61573010)the Fund of Sichuan University of Science and Engineering(No.2015RC10)+1 种基金the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(No.2014QZJ03)the Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things(No.2016WYJ04)
文摘The authors compute non-zero structure constants of the full flag manifold M = SO(7)/T with nine isotropy summands,then construct the Einstein equations.With the help of computer they get all the forty-eight positive solutions(up to a scale) for SO(7)/T,up to isometry there are only five G-invariant Einstein metrics,of which one is Khler Einstein metric and four are non-Khler Einstein metrics.
文摘Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E’=E|<sub> \D</sub> compatible with the parabolic structure, whose curvature is square integrable.
基金supported by National Natural Science Foundation of China(Grant Nos.11401425,11626134,11701300,11671212 and 51535008)K.C.Wong Magna Fund in Ningbo University。
文摘In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some very special cases,the coset space G×G/△(K)carries at least two invariant Einstein metrics.Furthermore,in the case that G1,G2 and K are simple Lie groups,with K■G1,K■G2,and G_1≠G2,such that G_1/K and G2/K are compact isotropy irreducible spaces,we give a complete classification of invariant Einstein metrics on the coset space G1×G2/△(K).
基金supported by Ministry of Education and Sciences of the Republic of Kazakhstan for 2015–2017 (Agreement N 299, February 12, 2015) (Grant No. 1452/GF4)
文摘Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l+ m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there are infinitely many spaces of the type SO(k + l + m)/SO(k)× SO(l) × SO(m) admitting exactly two, three, or four invariant Einstein metrics up to a homothety.
基金Projectsupported in part by NSF of China(Grant NO.10471097 and the Doctoral Programme Foundation of NEM of China
文摘The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-Khler metric on the special type of Hua domains is given and the sharp estimate of holomorphic sectional curvature under this metric is also obtained.In the meantime we also prove that the complete Einstein-Khler metric is equivalent to the Bergman metric on the special type of Hua domain.
文摘We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein＇s prescription in general relativity. As required for the Einstein energy-momentum complex, we perform the calculations in quasi-Cartesian coordinates. We also calculate the momentum components and obtain a zero value, as expected from the geometry of the metric.
