A pr 2 00 3 Immersions with fractal set of points of zero Gauss - Kronecker curvature
نویسندگان
چکیده
We construct, for any " good " Cantor set F of S n−1 , an immersion of the sphere S n with set of points of zero Gauss-Kronecker curvature equal to F ×D 1 , where D 1 is the 1-dimensional disk. In particular these examples show that the theorem of Matheus-Oliveira strictly extends two results by do Carmo-Elbert and Barbosa-Fukuoka-Mercuri.
منابع مشابه
Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter space or anti-de Sitter space
Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and oriented spacelike hypersurface in a de Sitter space or an anti-de Sitter space, $S$ and $K$ be the squared norm of the second fundamental form and Gauss-Kronecker curvature of $M^n$. If $S$ or $K$ is constant, nonzero and $M^n$ has two distinct principal curvatures one of which is simple, we obtain some charact...
متن کاملar X iv : 0 80 5 . 24 33 v 1 [ m at h . A P ] 1 6 M ay 2 00 8 ISOMETRIC IMMERSIONS AND COMPENSATED
A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold M which can be realized as isometric immersions into R. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptichyperbolic type whose mathematical theory is largely incomplete. In t...
متن کاملM ar 2 00 3 Immersions of Arbitrary Constant Mean Curvature in Hyperbolic Space H 3 ( − 1 )
Our work studies immersions of arbitrary constant mean curvature in H3(−1), as integrable surfaces (i.e., associate families of surfaces). We first present new results related to isometric deformations within this category of surfaces. Next, we give a Weierstrass type representation formula for these immersions. Ultimately, we discuss correspondences between such immersions in Euclidean 3-space...
متن کاملIsometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature
The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in L∞ are obtained through the vanishing viscosity method and the compensated compactness framework. The L∞ uniform estimate and H−1 compactness are ...
متن کاملSliding Friction Contact Stiffness Model of Involute Arc Cylindrical Gear Based on Fractal Theory
Gear’s normal contact stiffness played an important role in the mechanical equipment. In this paper, the M-B fractal model is modified and the contact surface coefficient is put forward to set up the fractal model, considering the influence of friction, which could be used to calculate accurately the involute arc cylindrical gears’ normal contact stiffness based on the fractal theory and Hertz ...
متن کامل