Displaying similar documents to “A lossless reduction of geodesics on supermanifolds to non-graded differential geometry”

On a theorem of Fermi

Viktor V. Slavskii (1996)

Commentationes Mathematicae Universitatis Carolinae


Conformally flat metric g ¯ is said to be Ricci superosculating with g at the point x 0 if g i j ( x 0 ) = g ¯ i j ( x 0 ) , Γ i j k ( x 0 ) = Γ ¯ i j k ( x 0 ) , R i j k ( x 0 ) = R ¯ i j k ( x 0 ) , where R i j is the Ricci tensor. In this paper the following theorem is proved: ((

Invariance of g -natural metrics on linear frame bundles

Oldřich Kowalski, Masami Sekizawa (2008)

Archivum Mathematicum


In this paper we prove that each g -natural metric on a linear frame bundle L M over a Riemannian manifold ( M , g ) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define g -natural metrics on the orthonormal frame bundle O M and we prove the same invariance result as above for O M . Hence we see that, over a space ( M , g ) of constant sectional curvature, the bundle O M with an arbitrary g -natural metric G ˜ is locally homogeneous.

Notes on prequantization of moduli of G -bundles with connection on Riemann surfaces

Andres Rodriguez (2004)

Annales mathématiques Blaise Pascal


Let 𝒳 S be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and a G -bundle over 𝒳 with connection along the fibres 𝒳 S . We construct a line bundle with connection ( , ) on S (also in cases when the connection on has regular singularities). We discuss the resulting ( , ) mainly in the case G = * . For instance when S is the moduli space of line bundles with connection over a Riemann surface X , 𝒳 = X × S , and is the Poincaré bundle over 𝒳 , we show that ( , ) provides a prequantization...

On symmetrization of jets

Włodzimierz M. Mikulski (2011)

Czechoslovak Mathematical Journal


Let F = F ( A , H , t ) and F 1 = F ( A 1 , H 1 , t 1 ) be fiber product preserving bundle functors on the category ℱℳ m of fibred manifolds Y with m -dimensional bases and fibred maps covering local diffeomorphisms. We define a quasi-morphism ( A , H , t ) ( A 1 , H 1 , t 1 ) to be a G L ( m ) -invariant algebra homomorphism ν : A A 1 with t 1 = ν t . The main result is that there exists an ℱℳ m -natural transformation F Y F 1 Y depending on a classical linear connection on the base of Y if and only if there exists a quasi-morphism ( A , H , t ) ( A 1 , H 1 , t 1 ) . As applications, we study existence problems of symmetrization (holonomization)...