分类： 数学 >> 几何与拓扑 提交时间： 2024-02-28
摘要： In this paper, we study biharmonic Riemannian submersions $ pi:M^2 times r to (N^2,h)$ from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, then a proper biharmonic Riemannian submersion $ pi:M^2 times r to (N^2,h)$ is locally a projection of a special twisted product, and when the target surface is non-flat, $ pi$ is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion $H^2 times r to r^2$ given by the projection of a warped product.
分类： 数学 >> 几何与拓扑 提交时间： 2023-02-22
摘要： In this paper, we give a complete classifification of harmonic and biharmon#2; ic Riemannian submersions : (R^3 , g_Sol) (N^2 , h) from Sol space into a surface by proving that there is neither harmonic nor biharmonic Riemann#2; ian submersion : (R^3 , g_Sol) (N^2 , h) from Sol space no matter what the base space (N2 , h) is. We also prove that a Riemannian submersion : (R^3 , g_Sol) (N^2 , h) from Sol space exists only when the base space is a hyperbolic space form.
分类： 数学 >> 几何与拓扑 提交时间： 2023-02-22
摘要： In this paper, we study biharmonic isometric immersions of a surface into and biharmonic Riemannian submersions from 3-dimensional Berger spheres. We obtain a classifification of proper biharmonic isometric immersions of a surface with constant mean curvature into Berger 3-spheres. We also give a complete classifification of proper biharmonic Hopf tori in Berger 3-sphere. For Riemannian submersions, we prove that a Riemannian submersion from Berger 3-spheres into a surface is biharmonic if and only if it is harmonic.
分类： 数学 >> 几何与拓扑 提交时间： 2022-10-12
摘要： 本文给出了若干四元数体射影平面的多重双角锥的非稳定同伦群。
分类： 医学、药学 >> 医学、药学其他学科 分类： 数学 >> 几何与拓扑 分类： 计算机科学 >> 计算机科学的集成理论 提交时间： 2018-03-31
摘要： Labeled images are one of the most important means of scientific communication and education. However, traditional markers (arrows, lines) are point markers; do not include information about how large the feature is. We designed an efficient marker system for labeling scientific images (electron or light microscopy, CT, MRI, ultrasonography, camera pictures, etc), called the “T Area Marker, (TAM)”. The basic TAM marker looks like a “T”, composed of a line segment and a small tick on one end; it defines an imagined circle that stands on the tickless end and the diameter of the circle is equal to the length of the line segment. Thus the TAM can define an exact area rather than a single point; and the imagined circle does not break the continuity of the image (unlike traditional visible circles, rectangles, etc). A TAM with N ticks (N>1) means the diameter equals to N times the length of TAM. A TAM may also have a tail and/or several tail branches to define translation of the imagined circle, thus define complicated areas. tAreaMarker.py is free software that combines the drawing and reading of TAMs, although in most cases TAMs are easily interpreted without computer assistance.
分类： 数学 >> 几何与拓扑 提交时间： 2017-11-23
摘要： 这篇文章中，首先给出了局部对称Lorentz空间中线性 Weingarten类空超曲面的数量曲率和平均曲率的关系。进而，我们研究了局部对称Lorentz空间中满足一定曲率的完备或者紧致线性 Weingarten类空超曲面，通过修改Cheng-Yau的算子，给出了一些新的估计。最终，我们在局部对称Lorentz空间中给出了一些猜想的部分推广。
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