We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case.
This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.
In the present paper we have obtained the necessary condition for the existence of almost pseudo symmetric and almost pseudo Ricci symmetric Sasakian manifold admitting a type of quarter symmetric metric connection.
To any smooth compact manifold endowed with a contact structure and partially integrable almost CR structure , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric on . We consider the asymptotic expansion, in powers of a special defining function, of the volume of with respect to and prove that the log term coefficient is independent of (and any choice of contact...