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Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group

Stefan Ivanov, Ivan Minchev and Dimiter Vassilev

Vol. 16 (2023), No. 3, 839–860
Abstract

A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension 4n+3 as well as on the quaternionic Heisenberg group is given. A uniqueness theorem for the qc Yamabe problem in a compact locally 3-Sasakian manifold is shown.

Keywords
Yamabe equation, quaternionic contact structures, Einstein structures, divergence formula, Folland–Stein inequality, Heisenberg group
Mathematical Subject Classification
Primary: 53C17
Milestones
Received: 13 February 2021
Accepted: 1 September 2021
Published: 25 May 2023
Authors
Stefan Ivanov
Faculty of Mathematics and Informatics
University of Sofia
Sofia
Bulgaria
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Sofia
Bulgaria
Department of Mathematics
University of Pennsylvania
Philadelphia, PA
United States
Ivan Minchev
Faculty of Mathematics and Informatics
University of Sofia
Sofia
Bulgaria
Department of Mathematics and Statistics
Masaryk University
Brno
Czech Republic
Dimiter Vassilev
Department of Mathematics and Statistics
University of New Mexico
Albuquerque, NM
United States

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