منابع مشابه
On Surfaces with Prescribed Shape Operator
The problem of immersing a simply connected surface with a prescribed shape operator is discussed. It is shown that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimens...
متن کاملHypersurfaces of a Sasakian space form with recurrent shape operator
Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.
متن کاملOn Surfaces of Prescribed F-Mean Curvature
Hypersurfaces of prescribed weighted mean curvature, or F -mean curvature, are introduced as critical immersions of anisotropic surface energies, thus generalizing minimal surfaces and surfaces of prescribed mean curvature. We first prove enclosure theorems in R for such surfaces in cylindrical boundary configurations. Then we derive a general second variation formula for the anisotropic surfac...
متن کاملOn Surfaces of Prescribed Weighted Mean Curvature
Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and von der Mosel. Next we study graphs of prescribed weighted mean curvature, for ...
متن کاملA note on surfaces with prescribed oriented Euclidean Gauss map
We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. Our approach depends on geometric quantities, that is, the hyperbolic Gauss map G and formulae obtained in hyperbolic space. We use the idea that the Euclidean Gauss map and the hyperbolic Gauss map with some compatibility relation determin...
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2001
ISSN: 0378-6218,1420-9012
DOI: 10.1007/bf03322701