A canonical connection on sub-Riemannian contact manifolds

Michael Eastwood and Katharina Neusser

School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
Eduard Čech Institute & Mathematical Institute, Charles University, Prague, Czech Republic


Abstract: 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.

AMSclassification: primary 53C17; secondary 53D10, 70G45.

Keywords: contact manifold, sub-Riemannian geometry, partial connection, pseudo-Hermitian geometry.

DOI: 10.5817/AM2016-5-277