Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of ...Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn +pwith parallel nor- malized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.展开更多
This paper advances a new algorithm oriented to geometry modeling (GM) by using frame model. The elemental data structure of frame model is the vertex. This afeoithm provides a general and rapid method. By this way,we...This paper advances a new algorithm oriented to geometry modeling (GM) by using frame model. The elemental data structure of frame model is the vertex. This afeoithm provides a general and rapid method. By this way,we can link the vertices to construct the elemental frame and need not consider the topological relation among vertices which consist of the concrete entity. Then, we can combine the elemental frames to complete frame modeling by using aided-line method referring to concrete entity. We will discuss two keystones in the paper. Then we give a 3D geometry modeling example based on wire-frame model using the new algorithm.展开更多
基金Project supported by the Stress Supporting Subject Foundation of Zhejiang Province, China
文摘Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn +pwith parallel nor- malized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.
文摘This paper advances a new algorithm oriented to geometry modeling (GM) by using frame model. The elemental data structure of frame model is the vertex. This afeoithm provides a general and rapid method. By this way,we can link the vertices to construct the elemental frame and need not consider the topological relation among vertices which consist of the concrete entity. Then, we can combine the elemental frames to complete frame modeling by using aided-line method referring to concrete entity. We will discuss two keystones in the paper. Then we give a 3D geometry modeling example based on wire-frame model using the new algorithm.
