symplectic

Adjective

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Adjective

**symplectic** (*not comparable*)

- Placed in or among, as if woven together.
- (
*group theory, of a group*) Whose characteristic abelian subgroups are cyclic. - (
*mathematics, multilinear algebra, of a bilinear form*) That is alternating and nondegenerate. - (
*mathematics, multilinear algebra, of a vector space*) That is equipped with an alternating nondegenerate bilinear form. - (
*mathematics*) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.**1995**, V. I. Arnold,*Some remarks on*, Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder (editors),**symplectic**monodromy of Milnor fibrations*The Floer Memorial Volume*, Birkhäuser Verlag, page 99 ↗,- There exist interesting and unexplored relations between
**symplectic**geometry and the theory of critical points of holomorphic functions.

- There exist interesting and unexplored relations between
**1997**, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau,*Structure of Dynamical Systems: A*, Springer Science & Business Media (Birkhäuser).**Symplectic**View of Physics**2003**, Fabrizio Catanese, Gang Tian (editors),**Symplectic**4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School ↗, Springer, Lecture Notes in Mathematics No. 1938.**2003**, Yakov Eliashberg, Boris A. Khesin, François Lalonde (editors),, American Mathematical Society.**Symplectic**and Contact Topology: Interactions and Perspectives ↗**2003**, Maung Min-Oo,*The Dirac Operator in Geometry and Physics*, Steen Markvorsen, Maung Min-Oo (editors),*Global Riemannian Geometry: Curvature and Topology*, Springer, page 72 ↗,- In
**symplectic**geometry, there is a notion of fibrations \pi : P \rightarrow M with a**symplectic**manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called**symplectic**fibrations. If the base manifold (M,\omega_M) is also**symplectic**, there is a weak coupling construction, originally due to Thurston, of defining a**symplectic**structure on the total space P.

- In

- That moves in the same direction as a system of synchronized waves.
- (
*petrology, mineralogy*) Of or pertaining to a symplectite; symplectitic.

**symplectic** (*plural* symplectics)

- (
*mathematics*) A symplectic bilinear form, manifold, geometry, etc.**1967**,*Indiana University Mathematics Journal, Volume 16, Issue 1*, Indiana University, page 339 ↗,- The structure of stable
**symplectics**on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.

- The structure of stable

- (
*ichthyology*) A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held.**1914**,*The Philippine Journal of Science, Volume 9*, page 27 ↗,- The
**symplectics**(9) consist of a somewhat curved central triangular portion with the base upward, and anteriorly and posteriorly from this extends a wing-like process.

- The
**1965**,*Agra University Journal of Research: Science, Volume 14*, page 71 ↗,- The
**symplectics**(Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.

- The
**1967**, Tyson R. Roberts,*Studies on the Osteology and Phylogeny of Characoid Fishes*, page 59 ↗,- In many teleosts, on the other hand, including the catfishes, the
**symplectics**have been entirely lost.

- In many teleosts, on the other hand, including the catfishes, the

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002