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On some rational fibrations with nonvanishing Massey products over homogeneous spaces

Tralle, Alexei (1994)

Proceedings of the Winter School "Geometry and Physics"

The main result of this brief note asserts, incorrectly, that there exists a rational fibration S 2 E P 3 whose total space admits nonzero Massey products. The methods used would be appropriate for showing results of this kind, if the circumstances were to allow for it. Unfortunately the author makes a simple, but nonetheless fatal, computational error in his calculation that ostensibly shows the existence of a nonzero Massey product (p. 249, 1.13: a b D ( x 2 y ) ) . In fact, for any rational fibration S 2 E P 3 the total space...

On some relations between curvature and metric tensors in Riemannian spaces

Mikeš, Josef, Laitochová, Jitka, Pokorná, Olga (2000)

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

The paper generalizes results of H. H. Hacisalihoglu and A. Kh. Amirov [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in n given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a...

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...

Currently displaying 941 – 960 of 1552