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Integral geometry for the taxicab metric
Integral geometry taxicab metric
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2011/3/1
Classical integral geometry takes place in Rn equipped with the Euclidean metric. We begin to develop integral geometry for Rn equipped with the taxicab metric (induced by the 1-norm).
Basic Riemannian Geometry and Sobolev Estimates used in Symplectic Topology
Basic Riemannian Geometry Sobolev Estimates used Symplectic Topology
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2011/2/22
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace
theory that play a prominent role in analytic approaches to symplectic topology. These
include relations...
On the spectral geometry of a Riemannian Legendre foliation
spectral geometry Riemannian Legendre foliation
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2010/12/8
We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant '-sectional curvature.
The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
almost-Riemannian geometry conjugate and cut loci
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2010/12/6
We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Rieman-nian geometry. We compute estimations of the exponential map wh...
Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE
Conformal geometry of surfaces Lagrangian--Grassmannian and second order PDE
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2010/12/1
Of all real Lagrangian{Grassmannians LG(n; 2n), only LG(2; 4) admits a distinguished Lorentzian) conformal structure and hence is identi ed with the inde nite Mobius space S1;2.
Almost commutative Riemannian geometry, I: wave operators
noncommutative geometry quantum groups quantum gravity
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2010/12/3
Associated to any (pseudo)-Riemannian manifold M of dimension n is an n + 1-dimensional noncommutative di erential structure (1; d)on the manifold.
Special Lagrangian Geometry in irreducible symplectic 4-folds
Lagrangian Geometry irreducible symplectic 4-folds
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2010/10/29
Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they ...