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Deformations of minimal surfaces of $𝐑^{3}$ containing planar geodesics

Gollek, Hubert (1999)

Proceedings of the 18th Winter School "Geometry and Physics"

Derivations on the Nijenhuis-Schouten bracket algebra

Vanžura, Jiří (1990)

Proceedings of the Winter School "Geometry and Physics"

Derived algebra of the Frölicher-Nijenhuis bracket algebra

Vanžura, Jiří (1991)

Proceedings of the Winter School "Geometry and Physics"

Differential geometry over the structure sheaf: a way to quantum physics

Fischer, Gerald (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

An idea for quantization by means of geometric observables is explained, which is a kind of the sheaf theoretical methods. First the formulation of differential geometry by using the structure sheaf is explained. The point of view to get interesting noncommutative observable algebras of geometric fields is introduced. The idea is to deform the algebra $C^{\infty} (M, ℝ)$ by suitable interaction structures. As an example of such structures the Poisson-structure is mentioned and this leads naturally to deformation...

Disconnections of plane continua

Bajguz, W. (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

The paper deals with locally connected continua $X$ in the Euclidean plane. Theorem 1 asserts that there exists a simple closed curve in $X$ that separates two given points $x$ , $y$ of $X$ if there is a subset $L$ of $X$ (a point or an arc) with this property. In Theorem 2 the two points $x$ , $y$ are replaced by two closed and connected disjoint subsets $A$ , $B$ . Again – under some additional preconditions – the existence of a simple closed curve disconnecting $A$ and $B$ is stated.