منابع مشابه
Simply-connected Nonpositive Curved Surfaces in R3
where |B| is the length of second fundamental form. |B|2 = 4|H|2 − 2K, where H is the mean curvature and K is the Gauss curvature. The curvature of minimal surfaces is nonpositive. Then we exam what is still hold for some minimal surface theorems if extending the minimal condition H ≡ 0 to the surfaces with K ≤ 0 and (1). In 2001, F. Xavier [18] has the following theorem: Theorem [Xavier]. Let ...
متن کاملComplete Properly Embedded Minimal Surfaces in R3
In this short paper, we apply estimates and ideas from [CM4] to study the ends of a properly embedded complete minimal surface 2 ⊂ R3 with finite topology. The main result is that any complete properly embedded minimal annulus that lies above a sufficiently narrow downward sloping cone must have finite total curvature. In this short paper, we apply estimates and ideas from [CM4] to study the en...
متن کاملSomeNewDevelopments of Realization of Surfaces into R3
This paper intends to give a brief survey of the developments on realization of surfaces into R in the last decade. As far as the local isometric embedding is concerned, some results related to the Schlaffli-Yau conjecture are reviewed. As for the realization of surfaces in the large, some developments on Weyl problem for positive curvature and an existence result for realization of complete ne...
متن کاملIntersection Curves of Implicit and Parametric Surfaces in R3
We present algorithms for computing the differential geometry properties of Frenet apparatus and higher-order derivatives of intersection curves of implicit and parametric surfaces in 3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given an...
متن کاملLines of principal curvature on canal surfaces in R3.
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R3. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated...
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ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 1996
ISSN: 1340-6116
DOI: 10.2206/kyushujm.50.533