scholarly journals Infinitely many leaf-wise intersections on cotangent bundles

2012 ◽  
Vol 30 (2) ◽  
pp. 168-181 ◽  
Author(s):  
Peter Albers ◽  
Urs Frauenfelder
Keyword(s):  
Cotangent Bundles

scholarly journals The Role of the Legendre Transform in the Study of the Floer Complex of Cotangent Bundles

2014 ◽  
Vol 68 (11) ◽  
pp. 1885-1945 ◽  
Author(s):  
Alberto Abbondandolo ◽  
Matthias Schwarz
Keyword(s):  
Legendre Transform ◽  
Cotangent Bundles

scholarly journals The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

2016 ◽  
Vol 08 (03) ◽  
pp. 545-570 ◽  
Author(s):  
Luca Asselle ◽  
Gabriele Benedetti
Keyword(s):  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Symplectic Form ◽  
Critical Value ◽  
Closed Manifold ◽  
Hamiltonian Flow ◽  
Cotangent Bundles ◽  
Almost All

Let [Formula: see text] be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian [Formula: see text] and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if [Formula: see text] is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of [Formula: see text].

Quantum fluctuations of the metric, three-geometries and conformal embeddings in four-manifolds

2021 ◽  
Author(s):  
Simon Davis
Keyword(s):  
Path Integrals ◽  
Invariance Group ◽  
Two Dimensional ◽  
Four Dimensions ◽  
Physical Conditions ◽  
Exponential Expansion ◽  
Cotangent Bundles ◽  
Four Manifolds ◽  
Conformal Embeddings ◽  
Natural Relation

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of [Formula: see text], which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be [Formula: see text], [Formula: see text] and [Formula: see text] with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

Nef cotangent bundles over line arrangements

1988 ◽  
Vol 62 (3) ◽  
pp. 369-374
Author(s):  
Michael J. Spurr
Keyword(s):  
Line Arrangements ◽  
Cotangent Bundles

scholarly journals An Application of Spherical Geometry to Hyperkähler Slices

2020 ◽  
pp. 1-30
Author(s):  
Peter Crooks ◽  
Maarten van Pruijssen
Keyword(s):  
Sufficient Conditions ◽  
Compact Subgroup ◽  
Spherical Geometry ◽  
Spherical Subgroup ◽  
Cotangent Bundles ◽  
Complex Semisimple ◽  
Reductive Subgroup ◽  
Necessary And Sufficient

Abstract This work is concerned with Bielawski’s hyperkähler slices in the cotangent bundles of homogeneous affine varieties. One can associate such a slice with the data of a complex semisimple Lie group  $G$ , a reductive subgroup $H\subseteq G$ , and a Slodowy slice $S\subseteq \mathfrak{g}:=\text{Lie}(G)$ , defining it to be the hyperkähler quotient of $T^{\ast }(G/H)\times (G\times S)$ by a maximal compact subgroup of  $G$ . This hyperkähler slice is empty in some of the most elementary cases (e.g., when $S$ is regular and $(G,H)=(\text{SL}_{n+1},\text{GL}_{n})$ , $n\geqslant 3$ ), prompting us to seek necessary and sufficient conditions for non-emptiness. We give a spherical-geometric characterization of the non-empty hyperkähler slices that arise when $S=S_{\text{reg}}$ is a regular Slodowy slice, proving that non-emptiness is equivalent to the so-called $\mathfrak{a}$ -regularity of $(G,H)$ . This $\mathfrak{a}$ -regularity condition is formulated in several equivalent ways, one being a concrete condition on the rank and complexity of $G/H$ . We also provide a classification of the $\mathfrak{a}$ -regular pairs $(G,H)$ in which $H$ is a reductive spherical subgroup. Our arguments make essential use of Knop’s results on moment map images and Losev’s algorithm for computing Cartan spaces.

On symplectic submanifolds of cotangent bundles

1993 ◽  
Vol 29 (4) ◽  
pp. 271-279 ◽  
Author(s):  
Mark J. Gotay
Keyword(s):  
Cotangent Bundles
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