Para-CR structures on almost paracontact metric manifolds
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Joanna Wełyczko
Abstract
Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.
I would like to thank my supervisor Professor Zbigniew Olszak for his support and suggestions during this work.
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- Hille–Wintner type comparison criteria for the half-linear differential equations of third order
- Para-CR structures on almost paracontact metric manifolds
- Growth and Lδ-approximation of solutions of the Helmholtz equation in a finite disk
- Products of Świątkowski and quasi-continuous functions
- q-nonuniform difference linear control systems
- Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations
- Wolfe-type second-order fractional symmetric duality
- On nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces
Articles in the same Issue
- Frontmatter
- Hille–Wintner type comparison criteria for the half-linear differential equations of third order
- Para-CR structures on almost paracontact metric manifolds
- Growth and Lδ-approximation of solutions of the Helmholtz equation in a finite disk
- Products of Świątkowski and quasi-continuous functions
- q-nonuniform difference linear control systems
- Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations
- Wolfe-type second-order fractional symmetric duality
- On nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces
