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On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative
On the contact equivalence problem of second order ODEs quadratic second order derivative Differential Geometry
2012/6/19
In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the...
Adapted connections on metric contact manifolds
Adapted connections metric contact manifolds Differential Geometry
2012/4/16
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-form...
On prolongations of contact manifolds
prolongations of contact manifolds Symplectic Geometry Differential Geometry
2011/9/23
Abstract: In this note, we apply spectral sequences to both derive an obstruction to the existence of $n$-fold prolongations and to derive a topological classification. Prolongations were formerly use...
The Intrinsic Geometry of Almost Contact Metric Manifolds
almost contact manifold Sasakian manifold K-contact manifold the intrinsic geometry of almost contact metric manifolds
2011/9/22
Abstract: In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of...
Contact structures on principal circle bundles
principal circle bundles Symplectic Geometry
2011/9/20
Abstract: We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all ...
A note on the volume flux of smooth and continuous strictly contact isotopies
Flux homomorphism strictly contact isotopy regular contact form topological or continuous Hamiltonian
2011/9/20
Abstract: This note on the flux homomorphism for strictly contact isotopies complements the recent paper [MS11a] by P. Spaeth and the author. We determine the volume flux restricted to symplectic and ...
K-homology and index theory on contact manifolds
K-homology and index theory Operator Algebras Differential Geometry
2011/8/31
Abstract: Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index proble...
Lectures on Holomorphic Curves in Symplectic and Contact Geometry
Holomorphic Curves Symplectic Contact Geometry
2010/11/12
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incom...