In this note we discuss various canonical metrics on complex manifolds. A generalization of the Bergman metric is proposed and the relations of metrics on moduli spaces are commented. At last, we review some existence...In this note we discuss various canonical metrics on complex manifolds. A generalization of the Bergman metric is proposed and the relations of metrics on moduli spaces are commented. At last, we review some existence theorems of solutions to the Strominger system.展开更多
In this paper,we prove the existence of solutions to the Fu-Yau equation on com-pact Kähler manifolds.As an application,we give a class of non-trivial solutions of the modified Strominger system.
A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kèahler when the constant is non-zero and must be Chern flat when the co...A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kèahler when the constant is non-zero and must be Chern flat when the constant is zero.The conjecture is known in complex dimension 2 by the work of Balas-Gauduchon in 1985(when the constant is zero or negative)and by Apostolov±Davidov±Muskarov in 1996(when the constant is positive).For higher dimensions,the conjecture is still largely unknown.In this article,we restrict ourselves to pluriclosed manifolds,and confirm the conjecture for the special case of Strominger Kèahler-like manifolds,namely,for Hermitian manifolds whose Strominger connection(also known as Bismut connection)obeys all the Kaèhler symmetries.展开更多
In this paper,we consider the adiabatic limit of Fu–Yau equations on a product of two Calabi–Yau manifolds.We prove that the adiabatic limit of Fu–Yau equations are quasilinear equations.
文摘In this note we discuss various canonical metrics on complex manifolds. A generalization of the Bergman metric is proposed and the relations of metrics on moduli spaces are commented. At last, we review some existence theorems of solutions to the Strominger system.
文摘In this paper,we prove the existence of solutions to the Fu-Yau equation on com-pact Kähler manifolds.As an application,we give a class of non-trivial solutions of the modified Strominger system.
基金supported by NSFC(Grant No.12071050)Chongqing Normal University。
文摘A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kèahler when the constant is non-zero and must be Chern flat when the constant is zero.The conjecture is known in complex dimension 2 by the work of Balas-Gauduchon in 1985(when the constant is zero or negative)and by Apostolov±Davidov±Muskarov in 1996(when the constant is positive).For higher dimensions,the conjecture is still largely unknown.In this article,we restrict ourselves to pluriclosed manifolds,and confirm the conjecture for the special case of Strominger Kèahler-like manifolds,namely,for Hermitian manifolds whose Strominger connection(also known as Bismut connection)obeys all the Kaèhler symmetries.
基金Supported by the project"Analysis and Geometry on Bundle"of Ministry of Science and Technology of the People’s Republic of China(Grant No.SQ2020YFA070080)NSF in China(Grant Nos.11625106,11571332and 11721101)。
文摘In this paper,we consider the adiabatic limit of Fu–Yau equations on a product of two Calabi–Yau manifolds.We prove that the adiabatic limit of Fu–Yau equations are quasilinear equations.
