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Czasopisma help

  1. 2 Open Mathematics

Autorzy help

  1. 2 Ganchev G.

  2. 2 Mihova V.

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  1. 1 2013

  2. 1 2008

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Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations

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Ganchev G., Mihova V.
Open Mathematics
|
2013
|
tom 11
|
nr 1
133-148
EN
On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten surfaces and obtain the natural non-linear partial differential equations describing them. We obtain a characterization of space-like surfaces, whose curvatures satisfy a linear relation, by means of their natural partial differential equations. We obtain the ten natural PDE’s describing all linear fractional space-like Weingarten surfaces.
2
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Kähler manifolds of quasi-constant holomorphic sectional curvatures

100%
Ganchev G., Mihova V.
Open Mathematics
|
2008
|
tom 6
|
nr 1
43-75
EN
The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kähler metrics is shown to be exactly the class of Kähler metrics whose potential function is only a function of the distance from the origin in ℂn. Finally we show that any rotational even dimensional hypersurface carries locally a natural Kähler structure which is of quasi-constant holomorphic sectional curvatures.
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