‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

‎based on a definition for circle in finsler space‎, ‎recently proposed by one of the present authors and z‎. ‎shen‎, ‎a natural definition of extrinsic sphere in finsler geometry is given and it is shown that a connected submanifold of a finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

In this paper, we propose a novel extrinsic calibration method for camera networks using a sphere as the calibration object. First of all, we propose an easy and accurate method to estimate the 3D positions of the sphere center w.r.t. the local camera coordinate system. Then, we propose to use orthogonal procrustes analysis to pairwise estimate the initial camera relative extrinsic parameters b...

Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of nonnegative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a...

For all \(k\in ]0,1[\), we construct a canonical bijection between the space of ramified coverings sphere hyperbolic type and complete immersed surfaces in 3-dimensional finite area constant extrinsic curvature equal to k. We show, furthermore, that this restricts homeomorphism over each stratum sphere.

The linear Weingarten condition with ellipticity for the mean curvature and extrinsic Gaussian on a surface in three-sphere can define Riemannian metric which is called elliptic metric. We established some local characterizations of round spheres tori immersed 3-dimensional unit sphere, along Laplace operator, spherical Gauss map associated