All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 11 Next

Displaying 201 – 220 of 238

Showing per page

Note on the classification theorems of g -natural metrics on the tangent bundle of a Riemannian manifold ( M , g )

Mohamed Tahar Kadaoui Abbassi (2004)

Commentationes Mathematicae Universitatis Carolinae

In [7], it is proved that all g -natural metrics on tangent bundles of m -dimensional Riemannian manifolds depend on arbitrary smooth functions on positive real numbers, whose number depends on m and on the assumption that the base manifold is oriented, or non-oriented, respectively. The result was originally stated in [8] for the oriented case, but the smoothness was assumed and not explicitly proved. In this note, we shall prove that, both in the oriented and non-oriented cases, the functions generating...

Notes on conformal differential geometry

Eastwood, Michael (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

This survey paper presents lecture notes from a series of four lectures addressed to a wide audience and it offers an introduction to several topics in conformal differential geometry. In particular, a very nice and gentle introduction to the conformal Riemannian structures themselves, flat or curved, is presented in the beginning. Then the behavior of the covariant derivatives under the rescaling of the metrics is described. This leads to Penrose’s local twistor transport which is introduced in...

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 ℱ a G -bundle over 𝒳 with connection along the fibres 𝒳 → S . We construct a line bundle with connection ( ℒ ℱ , ∇ ℱ ) on S (also in cases when the connection on ℱ has regular singularities). We discuss the resulting ( ℒ ℱ , ∇ ℱ ) mainly in the case G = ℂ * . For instance when S is the moduli space of line bundles with connection over a Riemann surface X , 𝒳 = X × S , and ℱ is the Poincaré bundle over 𝒳 , we show that ( ℒ ℱ , ∇ ℱ ) provides a prequantization of S .

Currently displaying 201 – 220 of 238