Volume of certain subsets of $T^*S^3$ The 2019 Stack Overflow Developer Survey Results Are Inis the geodesic flow on Hyperbolic Plane completely integrable?orientation of symplectic manifold and lagrangian submanifoldsTopology on the space of compatible almost complex structures in symplectic geometryTwo different definitions of a Liouville measureVolume of “the complex projective space” of a certain radius.Riemannian metric as an operatorHow to measure the norm of a section of a line bundle given a metric on the manifold?Why don't we consider “Hamiltonian vector field” on tangent bundle?When is a Divergence-Free Vector Field on the Tangent Bundle of a Riemannian Manifold Hamiltonian?Characterizations of Riemannian Volume Form
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Volume of certain subsets of $T^*S^3$
The 2019 Stack Overflow Developer Survey Results Are Inis the geodesic flow on Hyperbolic Plane completely integrable?orientation of symplectic manifold and lagrangian submanifoldsTopology on the space of compatible almost complex structures in symplectic geometryTwo different definitions of a Liouville measureVolume of “the complex projective space” of a certain radius.Riemannian metric as an operatorHow to measure the norm of a section of a line bundle given a metric on the manifold?Why don't we consider “Hamiltonian vector field” on tangent bundle?When is a Divergence-Free Vector Field on the Tangent Bundle of a Riemannian Manifold Hamiltonian?Characterizations of Riemannian Volume Form
$begingroup$
Consider $S^3$ equipped with the round metric of unit radius. The metric naturally gives a metric on the cotangent bundle, so we can consider the subset $$S_t = ^2 < t.$$ Now let $omega$ be the natural symplectic form on $T^*S^3$.
Question: How to calculate $int_S_t omega^3$ in terms of t?
This has definitely been considered before and is most probably in some book, so I am searching for a suitable reference (I cannot seem to find this calculation in McDuff-Salamons book).
differential-geometry reference-request symplectic-geometry
asked Mar 23 at 1:54
Nick LNick L
1,329210
$endgroup$
add a comment |
$begingroup$
Consider $S^3$ equipped with the round metric of unit radius. The metric naturally gives a metric on the cotangent bundle, so we can consider the subset $$S_t = ^2 < t.$$ Now let $omega$ be the natural symplectic form on $T^*S^3$.
Question: How to calculate $int_S_t omega^3$ in terms of t?
This has definitely been considered before and is most probably in some book, so I am searching for a suitable reference (I cannot seem to find this calculation in McDuff-Salamons book).
differential-geometry reference-request symplectic-geometry
asked Mar 23 at 1:54
Nick LNick L
1,329210
$endgroup$
add a comment |
$begingroup$
Consider $S^3$ equipped with the round metric of unit radius. The metric naturally gives a metric on the cotangent bundle, so we can consider the subset $$S_t = ^2 < t.$$ Now let $omega$ be the natural symplectic form on $T^*S^3$.
Question: How to calculate $int_S_t omega^3$ in terms of t?
This has definitely been considered before and is most probably in some book, so I am searching for a suitable reference (I cannot seem to find this calculation in McDuff-Salamons book).
differential-geometry reference-request symplectic-geometry
asked Mar 23 at 1:54
Nick LNick L
1,329210
$endgroup$
Consider $S^3$ equipped with the round metric of unit radius. The metric naturally gives a metric on the cotangent bundle, so we can consider the subset $$S_t = ^2 < t.$$ Now let $omega$ be the natural symplectic form on $T^*S^3$.
Question: How to calculate $int_S_t omega^3$ in terms of t?
This has definitely been considered before and is most probably in some book, so I am searching for a suitable reference (I cannot seem to find this calculation in McDuff-Salamons book).
differential-geometry reference-request symplectic-geometry
differential-geometry reference-request symplectic-geometry
asked Mar 23 at 1:54
Nick LNick L
1,329210
asked Mar 23 at 1:54
Nick LNick L
1,329210
asked Mar 23 at 1:54
Nick LNick L
1,329210
asked Mar 23 at 1:54
Nick LNick L
1,329210
asked Mar 23 at 1:54
Nick LNick L
1,329210
1,329210
add a comment |
add a comment |
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