In this paper, we continue to discuss the sufficient conditions for a compact Kaehler submanifold in a locally symmetric Bochner-Kaehler manifold to be totally geodesic. We have obtained the following results. Theorem...In this paper, we continue to discuss the sufficient conditions for a compact Kaehler submanifold in a locally symmetric Bochner-Kaehler manifold to be totally geodesic. We have obtained the following results. Theorem 1. Let M^(n+p) be a locally symmetric Bochner-Kaehler manifold of complex dimensions n+p and M^n a compact Kaehler submanifold of complex dimension (n≥2) in M^(n+p). Let and, where Ric(M)_x denotes the Ricci curvature of M^(n+p) at the point x. If the scalar curvature ρ_M of M^n satisfies then M^n must be totally geodesic in M^(n+p). Theorem 2. Let M^n and M^(n+p) be the same as those in Theorem 1. If the Ricci curvature Q_M of M^n satisfies then M^n is totally geodesic in M^(n+p).展开更多
Trace amount of Sr(0.05 wt.%)was added into the hypoeutectic Al−Si(3−12 wt.%Si)alloys to modify their microstructure and improve thermal conductivity.The results showed that the thermal conductivity of hypoeutectic Al...Trace amount of Sr(0.05 wt.%)was added into the hypoeutectic Al−Si(3−12 wt.%Si)alloys to modify their microstructure and improve thermal conductivity.The results showed that the thermal conductivity of hypoeutectic Al−Si alloys was improved by Sr modification,and the increment and increasing rate of the thermal conductivity gradually increased with Si content increasing.The improvement of thermal conductivity was primarily related to the morphology variation of eutectic Si phases.In Sr-modified Al−Si alloys,the morphology of eutectic Si phases was a mixed morphology of fiber structure and fine flaky structure,and the proportion of the fine flaky eutectic Si phases gradually decreased with Si content increasing.Under the Si content reaching 9 wt.%,the proportion of fine flaky eutectic Si phases was nearly negligible in Sr-modified alloys.Correspondingly,the increment and increasing rate of thermal conductivity of Sr-modified alloys reached the maximum and tended to be stable.展开更多
基金Supported by a Grant-in-Aid for Scientific Research from Nanjing University of Science and Technology(No.AB96137)apartially by the National Natural Science Foundation of China(No.10471063)
文摘In this paper, we continue to discuss the sufficient conditions for a compact Kaehler submanifold in a locally symmetric Bochner-Kaehler manifold to be totally geodesic. We have obtained the following results. Theorem 1. Let M^(n+p) be a locally symmetric Bochner-Kaehler manifold of complex dimensions n+p and M^n a compact Kaehler submanifold of complex dimension (n≥2) in M^(n+p). Let and, where Ric(M)_x denotes the Ricci curvature of M^(n+p) at the point x. If the scalar curvature ρ_M of M^n satisfies then M^n must be totally geodesic in M^(n+p). Theorem 2. Let M^n and M^(n+p) be the same as those in Theorem 1. If the Ricci curvature Q_M of M^n satisfies then M^n is totally geodesic in M^(n+p).
基金Project(2013B090500091)supported by Industry-University-Research Combined Project of Guangdong Province,ChinaProject(20180358)supported by the Shenzhen Jiansheng Technology Inc.Cooperation Project,China。
文摘Trace amount of Sr(0.05 wt.%)was added into the hypoeutectic Al−Si(3−12 wt.%Si)alloys to modify their microstructure and improve thermal conductivity.The results showed that the thermal conductivity of hypoeutectic Al−Si alloys was improved by Sr modification,and the increment and increasing rate of the thermal conductivity gradually increased with Si content increasing.The improvement of thermal conductivity was primarily related to the morphology variation of eutectic Si phases.In Sr-modified Al−Si alloys,the morphology of eutectic Si phases was a mixed morphology of fiber structure and fine flaky structure,and the proportion of the fine flaky eutectic Si phases gradually decreased with Si content increasing.Under the Si content reaching 9 wt.%,the proportion of fine flaky eutectic Si phases was nearly negligible in Sr-modified alloys.Correspondingly,the increment and increasing rate of thermal conductivity of Sr-modified alloys reached the maximum and tended to be stable.
