Subjects: Mathematics >> Geometry and Topology submitted time 2024-02-28
Abstract： 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.
Peer Review Status:
Awaiting Review
Subjects: Mathematics >> Geometry and Topology submitted time 2023-02-22
Abstract： In this paper, we give a complete classifification of harmonic and biharmon#2;
ic Riemannian submersions π : (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 π : (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
π : (R^3 , g_Sol) → (N^2 , h) from Sol space exists only when the base space is
a hyperbolic space form.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Geometry and Topology submitted time 2023-02-22
Abstract：
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.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Geometry and Topology submitted time 2022-10-12
Abstract：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。
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Other Disciplines of Medicine and Pharmacology Subjects: Mathematics >> Geometry and Topology Subjects: Computer Science >> Integration Theory of Computer Science submitted time 2018-03-31
Abstract： 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.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Geometry and Topology submitted time 2017-11-23
Abstract： In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces $M^{n}$ with $R=aH+b_{1}$ in a locally symmetric Lorentz space $L_{1}^{n+1}$, where $R$ and $H$ are the normalized scalar curvature and the mean curvature of $M^{n}$, respectively. Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces $L_{1}^{n+1}$ satisfying some curvature conditions. By modifying Cheng-Yau's operator $\square$ given in {\cite{ChengYau77}}, we introduce a modified operator $L$ and give new estimates of $L(nH)$ and $\square(nH)$ of such spacelike hypersurfaces. Finally, we give partial generalizations of some Conjectures in locally symmetric Lorentz spaces $L_{1}^{n+1}$.
Peer Review Status:Awaiting Review
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