Patra, D.S.; Rovenski, V. On the Rigidity of the Sasakian Structure and Characterization of Cosymplectic Manifolds. Differential Geometry and its Applications 2023, 90, 102043, doi:10.1016/j.difgeo.2023.102043.
Patra, D.S.; Rovenski, V. On the Rigidity of the Sasakian Structure and Characterization of Cosymplectic Manifolds. Differential Geometry and its Applications 2023, 90, 102043, doi:10.1016/j.difgeo.2023.102043.
Patra, D.S.; Rovenski, V. On the Rigidity of the Sasakian Structure and Characterization of Cosymplectic Manifolds. Differential Geometry and its Applications 2023, 90, 102043, doi:10.1016/j.difgeo.2023.102043.
Patra, D.S.; Rovenski, V. On the Rigidity of the Sasakian Structure and Characterization of Cosymplectic Manifolds. Differential Geometry and its Applications 2023, 90, 102043, doi:10.1016/j.difgeo.2023.102043.
Abstract
We introduce new metric structures on a smooth manifold (called “weak" structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures (φ,ξ,η,g) and allow us to take a fresh look at the classical theory and find new applications. This assertion is illustrated by generalizing several well-known results. It is proved that any Sasakian structure is rigid, i.e., our weak Sasakian structure is homothetically equivalent to a Sasakian structure. It is shown that a weak almost contact structure with parallel tensor φ is a weak cosymplectic structure and an example of such a structure on the product of manifolds is given. Conditions are found under which a vector field is a weak contact vector field.
Computer Science and Mathematics, Geometry and Topology
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