The symplectic Thom conjecture.
Ozsváth, Peter, Szabó, Zoltán (2000)
Annals of Mathematics. Second Series
Similarity:
Ozsváth, Peter, Szabó, Zoltán (2000)
Annals of Mathematics. Second Series
Similarity:
Viktor Ginzburg, Richard Montgomery (2000)
Banach Center Publications
Similarity:
A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....
Indranil Biswas (1997)
Annales de l'institut Fourier
Similarity:
The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.
Janyška, Josef
Similarity:
In this nice paper the author proves that all natural symplectic forms on the tangent bundle of a pseudo-Riemannian manifold are pull-backs of the canonical symplectic form on the cotangent bundle with respect to some diffeomorphisms which are naturally induced by the metric.
Ben Nasatyr, Brian Steer (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
Purcaru, Monica (2003)
Balkan Journal of Geometry and its Applications (BJGA)
Similarity:
Michor, P.W., Schichl, H. (1997)
Acta Mathematica Universitatis Comenianae. New Series
Similarity: