We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterizati...We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.展开更多
In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons＇ type inte- gral inequality of compact submanifoids as well a...In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons＇ type inte- gral inequality of compact submanifoids as well as some pinching theorems on＇the second fundamental form.展开更多
We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics.We prove that a compact locally conformal Kähler manifold with the constant nonpositive holomorphi...We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics.We prove that a compact locally conformal Kähler manifold with the constant nonpositive holomorphic sectional curvature is K?hler.We also give examples of complete non-Kähler metrics with pointwise negative constant but not globally constant holomorphic sectional curvature,and complete non-Kähler metrics with zero holomorphic sectional curvature and nonvanishing curvature tensors.展开更多
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
It is proved that, for any elementary torsion free Fuchsian group F, the natural projection from the Teichmiiller curve V（F） to the Teichmiiller space T（F） has no holomorphic section.
文摘We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.
基金Foundation item： Supported by the National Natural Science Foundation of China（ll071005） Supported by the Natural Science Foundation of Anhui Province Education Department（KJ2008A05zC）
文摘In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons＇ type inte- gral inequality of compact submanifoids as well as some pinching theorems on＇the second fundamental form.
基金supported by National Natural Science Foundation of China(Grant No.11801516)Zhejiang Provincial Natural Science Foundation(Grant No.LY19A010017)。
文摘We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics.We prove that a compact locally conformal Kähler manifold with the constant nonpositive holomorphic sectional curvature is K?hler.We also give examples of complete non-Kähler metrics with pointwise negative constant but not globally constant holomorphic sectional curvature,and complete non-Kähler metrics with zero holomorphic sectional curvature and nonvanishing curvature tensors.
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 Program for New Century Excellent Talents in University (Grant No.NCET-06-0504)National Natural Science Foundation of China (Grant No.10771153)
文摘It is proved that, for any elementary torsion free Fuchsian group F, the natural projection from the Teichmiiller curve V（F） to the Teichmiiller space T（F） has no holomorphic section.
