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Displaying 41 – 60 of 125

Harmonic spinors on Riemann surfaces

Bureš, Jarolím (1994)

Proceedings of the Winter School "Geometry and Physics"

Higher order almost tangent geometry and non-autonomous Lagrangian dynamics

de León, Manuel, Rodrigues, Paulo R. (1987)

Proceedings of the Winter School "Geometry and Physics"

Hochschild cohomology and quantization of Poisson structures

Grabowski, Janusz (1994)

Proceedings of the Winter School "Geometry and Physics"

It is well-known that the question of existence of a star product on a Poisson manifold $N$ is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures $P$ of the following type $P = X \land Y$ with $[X, Y] = u X + v Y$ , for some $u, v \in C^{\infty} (N, ℝ)$ .

Hopf structures on the Borel subalgebra of $s l (2)$

Ogievetsky, O. (1994)

Proceedings of the Winter School "Geometry and Physics"

Horizontal lifts and foliations

Pogoda, Zdzisław (1989)

Proceedings of the Winter School "Geometry and Physics"

Horizontal lifts of tensor fields and connections to the tangent bundle of higher order

Gancarzewicz, Jacek, Salgado, Modesto (1989)

Proceedings of the Winter School "Geometry and Physics"

Integral geometry for complexes of rational curves

Gindikin, S. G. (1989)

Proceedings of the Winter School "Geometry and Physics"

Invariance properties of the Laplace operator

Eichhorn, Jürgen (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions ${\bar{𝒞}}_{P}^{k}$ of the space $𝒞_{P}$ of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their...

Isospectral, non-isometric Riemannian manifolds

Schueth, Dorothea (1994)

Proceedings of the Winter School "Geometry and Physics"

The author gives a survey of the history of isospectral manifolds that are non-isometric discussing the work of Milnor, Vignéras, Sunada, and de Turck and Gordon. She describes the construction of continuous isospectral deformations as introduced by Gordon, Wilson, De Turck et al. She also discusses the construction of isospectral plane domains due to Gordon, Webb, and Wolpert. Some new examples of isospectral non-isometric manifolds are given.

Knit products of graded Lie algebras and groups

Michor, Peter W. (1990)

Proceedings of the Winter School "Geometry and Physics"

Let $A = ⨁_{k} A_{k}$ and $B = ⨁_{k} B_{k}$ be graded Lie algebras whose grading is in $𝒵$ or $𝒵_{2}$ , but only one of them. Suppose that $(α, β)$ is a derivatively knitted pair of representations for $(A, B)$ , i.e. $α$ and $β$ satisfy equations which look “derivatively knitted"; then $A \oplus B : = ⨁_{k, l} (A_{k} \oplus B_{l})$ , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra $A \oplus_{(α, β)} B$ . This graded Lie algebra is called the knit product of $A$ and $B$ . The author investigates the general situation for any graded Lie subalgebras $A$ and $B$ of a graded...