The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partiallypositive bisectional curvature without the assumption of nonnegative bisectional curvature.Some applications of the results to ...The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partiallypositive bisectional curvature without the assumption of nonnegative bisectional curvature.Some applications of the results to holomorphic mappings are given.展开更多
We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in...We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds.展开更多
We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Khler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian subm...We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Khler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Khler S^3× S^3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function λ, such that g((▽h)(v, v, v), J v) = λ holds for all unit tangent vector v.展开更多
文摘杂化弦的共形不变性和超共形不变性可用圈和超圈的微分同胚群 DiffS^1和Super-DiffS^1描述.基圈的重参数化形成商空间 M=DiffS^1/S^1和N=Super—DiffS^1/S^1.它们是无限维的 Kahler 流形和超 Kahler 流形.本文研究这些无限维流形的全纯几何.用陪集空间的技术讨论了它们的辛结构,通过在 M 和 N 上引入全纯坐标和夏结构我们计算了在原点邻域内的 Killing 矢量,给出了 M 和 N 上的Riemann 度规.这些结果在研究杂化弦的共形反常时有用.
文摘The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partiallypositive bisectional curvature without the assumption of nonnegative bisectional curvature.Some applications of the results to holomorphic mappings are given.
基金supported by Science Foundation of Guangdong Province (Grant No. S2012010010038)National Natural Science Foundation of China (Grant No. 11571215)supporting project from the Department of Education of Guangdong Province (Grant No. Yq2013073)
文摘We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds.
基金supported by National Natural Science Foundation of China (Grant No. 11371330)
文摘We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Khler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Khler S^3× S^3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function λ, such that g((▽h)(v, v, v), J v) = λ holds for all unit tangent vector v.
