A survey on cosymplectic geometry

Abstract

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

40 pages, table of contents

References in corpus (15)

• Contact manifolds and generalized complex structures
• Generalized Contact Structures
• Topology of 3-cosymplectic manifolds
• The curvature tensor of almost cosymplectic and almost Kenmotsu (κ,μ,ν)-spaces
• Unified formalism for non-autonomous mechanical systems
• 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem
• 3-quasi-Sasakian manifolds
• k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations
• Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds
• Bi-Legendrian manifolds and paracontact geometry
• The geometry of 3-quasi-Sasakian manifolds
• Reduction of symplectic principal $\mathbb{R}$-bundles
• Non-formal co-symplectic manifolds
• On CR (Cauchy-Riemann) almost cosymplectic manifolds
• On three dimensional conformally flat almost cosymplectic manifolds

Cited by in corpus (35)

• Contact Hamiltonian Systems
• Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• On nearly Sasakian and nearly cosymplectic manifolds
• Sasakian nilmanifolds
• Unified Lagrangian-Hamiltonian formalism for contact systems
• Almost co-Kähler manifolds and $(m,\rho )$-quasi-Einstein solitons
• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• Almost α-Paracosymplectic Manifolds
• Higher-order contact mechanics
• Contact Lie systems
• Noether symmetries and integrability in time-dependent Hamiltonian mechanics
• On Time-dependent Hamiltonian Realizations of Planar and Nonplanar Systems
• Generalized CoKähler Geometry and an Application to Generalized Kähler Structures
• Cosymplectic p-spheres
• On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
• Non-symmetric Riemannian gravity and Sasaki-Einstein 5-manifolds
• Poisson cohomology of a class of log symplectic manifolds
• Hamiltonian systems on almost cosymplectic manifolds
• Hereditary properties of co-Kähler manifolds
• Cosymplectic geometry, reductions, and energy-momentum methods with applications
• Parallel spinor flows on three-dimensional Cauchy hypersurfaces
• Classical KMS Functionals and Phase Transitions in Poisson Geometry
• Homogeneous G-structures
• Decomposable (6, 5)-solutions in eleven-dimensional supergravity
• Examples of 3-quasi-Sasakian manifolds
• Einstein-Weyl structures on almost cosymplectic manifolds
• On weakly Einstein almost contact manifolds
• K-cosymplectic manifolds
• Geometrical structures of higher-order dynamical systems and field theories
• Rank of Jacobi operator and existence of quadratic parallel differential form, with applications to geometry of almost para-contact metric manifolds
• Quasi-Einstein structures and almost cosymplectic manifolds
• A Discrete Variational Derivation of Accelerated Methods in Optimization
• Jacobi Sigma Models and Twisted Jacobi Structures
• Ricci solitons in almost $f$-cosymplectic manifolds