minimal immersion into a sphere by the first eigenfunctions as the extreme cases in several inequalities involving only the simplest spectral invariants: The first and the second eigenvalue of the Laplacian, the volume, the integral of the scalar curvature and the multiplicity of the first eigen...
Then we give a clear formula of the mean curvature of the surface in a Bao–Shen’s sphere by introducing the volume ratio function to show its ... N Cui - 《Geometriae Dedicata》 被引量: 7发表: 2014年 Towards a gravitation theory in Berwald-Finsler space We use the Bianchi identities...
53A0453A3553B30Semi-Euclidean spacecurvatures of curvesheight unfoldingdistance squared unfoldingWe show a formula for curvatures of curves in a semi-Euclidean space (or pseudo-sphere) with respect to Frenet–Serre type frame in terms of volumes. We also investigate versality of height unfolding ...
This ellipsoid determines a positive-definite scalar producthand a vectorin the sense that the ellipsoid coincides with the unit sphere ofhup to a translationof its center of mass to the origin. The pair (h,W) is called the Zermelo data of the Randers norm as it is related to the ...
As mentioned earlier, Example 1.3 shows that a sphere of radius r has k1=k2=-1/r (for U outward). Thus the sphere Σ has constant positive curvature K=1/r2: The smaller the sphere, the larger its curvature. We shall find many examples of these various special types of surface as we...
Model spaces of the surface theory are the surfaces with constant Gaussian Curvature. E.g. Euclidean Plane \mathbb{R}^{2} (K=0); Sphere of radius \mathbf{R} (K=1/R^{2}). Hyperbolic Plane: model surface with constant negative Gaussian Curvature. A plane that is hard to visualize beca...
In this paper, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry–Émery calculus. This flow can be adapted to preserve the Markovian property and its limits as time goes to infinity turn out to be curvature sharp
So, or I should put it at this location. So my new vector is this way and my old vector is that way. So that was a long winded way of showing that on a sphere, a curved surface, when you parallel transport a vector it doesn't come back pointing in the same direction. So what...
First, it is a top of a white sail; when it moves closer, you can also notice the shape of a ship. Where was this ship before? It was hidden behind the horizon. The reason for this is obvious: as Earth's shape is very similar to a sphere – the surface between you and the ...
n)-positivity of \mathring{R}, where C(p, n) is an explicit constant. In particular, it follows that a closed Riemannian n-manifold with \frac{n+2}{2}-nonnegative \mathring{R} is either flat or a rational homology sphere. Together with Wylie [...