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On sprays and connections

Kozma, László (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A connection structure (M,H) and a path structure (M,S) on the manifold M are called compatible, if S ( v ) = H ( v , v ) , v T M , locally G i ( x , y ) = y j Γ j i ( x , y ) , where G i and Γ j i express the semi-spray S and the connection map H, resp. In the linear case of H its geodesic spray S is quadratic: G i ( x , y ) = Γ j k i ( k ) y j y k . On the contrary, the homogeneity condition of S induces the relation for the compatible connection H, y j ( Γ j i μ t ) = t y j Γ j i , whence it follows not that H is linear, i.e. if a connection structure is compatible with a spray, then...

On the conformal relation between twistors and Killing spinors

Friedrich, Thomas (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The author considers the conformal relation between twistors and spinors on a Riemannian spin manifold of dimension n 3 . A first integral is constructed for a twistor spinor and various geometric properties of the spin manifold are deduced. The notions of a conformal deformation and a Killing spinor are considered and such a deformation of a twistor spinor into a Killing spinor and conditions for the equivalence of these quantities is indicated.

On the horizontal cohomology with general coefficients

Marvan, Michal (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A new cohomology theory suitable for understanding of nonlinear partial differential equations is presented. This paper is a continuation of the following paper of the author [Differ. geometry and its appl., Proc. Conf., Brno/Czech. 1986, Commun., 235-244 (1987; Zbl 0629.58033)].

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