Riemannian Geometry of Contact and Symplectic Manifolds
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5 citations
Cites background or result from "Riemannian Geometry of Contact and ..."
...This is not trivial, since the dimension of SE(2) is odd, and hence it can carry only an almost complex structure [6]: analyticity is then replaced by the weaker CR condition [4]....
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...If we denote by H the n-th Heisenberg group [14, 20] in its semidirect product form Rq o (Rp × Rt), defined by the group law (p′, q′, t′) · (p, q, t) = (p′ + p, q′ + q, t′ + t+ p′q) we note that, by an argument analogous to the one expressed for SE(2), we can associate to it a contact structure in the Darboux normal form [2, 6] ω0 = pdq − dt in accordance with the notion of H as a central extension of the commutative R....
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...The complex differentiability relies instead on the almost complex structure that can be associated to SE(2) as a contact manifold [6], and tells that PFΩ is a space of CR functions [4]....
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...This last one is not orientable and hence can not carry a global contact form [6], but it is useful to note that it arises naturally as the projectivization of the four dimensional phase space [2]....
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5 citations
5 citations
Cites background from "Riemannian Geometry of Contact and ..."
...For more details about almost contact Riemannian manifolds, we refer to [2]....
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5 citations
5 citations
Cites background from "Riemannian Geometry of Contact and ..."
...For more details, one can refer to ([1, 5, 36]) for instance....
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