Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group
Stefan Ivanov, Ivan Minchev, Dimiter Vassilev
TL;DR
This paper provides a complete solution to the quaternionic contact Yamabe equation on specific manifolds, establishing uniqueness results for the problem in compact 3-Sasakian manifolds.
Contribution
It offers the first complete solutions to the qc Yamabe equation on the qc sphere and quaternionic Heisenberg group, and proves a uniqueness theorem in compact 3-Sasakian manifolds.
Findings
Explicit solutions on the qc sphere and quaternionic Heisenberg group
Uniqueness of solutions in compact 3-Sasakian manifolds
Advancement in understanding the qc Yamabe problem
Abstract
A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension 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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic and Geometric Analysis · advanced mathematical theories